Water Quality Hazards and Dispersion of Pollutants 0387233210, 9780387233215

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WATER QUALITY HAZARDS AND DISPERSION OF POLLUTANTS Wlodzimierz Czernuszenko Pawel Rowinski

WATER QUALITY HAZARDS AND DISPERSION OF POLLUTANTS

WATER QUALITY HAZARDS AND DISPERSION OF POLLUTANTS

Edited by

Wlodzimierz Czernuszenko, Pawet M. Rowinski Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland

a 1E-02 5 1.E-03 50

100

150

200

250

300

350

Flow Rate (m3/s) Figure 4-7. Dispersion coefficients for in-bank case and for five over-bank flood plain widths (see legend).

4. Prediction of Dispersion Coefficients in a Compound Channel

6.5

81

Significance for pollutant transport

Finally, some indication of the impact on pollutant transport of the predicted flow dependence of dispersion coefficients in the channels used above is shown in Fig. 4-8. Here the maximum concentration of a contaminant patch at a location 10km downstream of a pollution incident is shown as a function of flow rate for four cases (in-bank, over-bank with flood plain width of 5m, over-bank with flood plain width of 20m and the extended trapezoidal channel case). The pollution incident consisted of the sudden release of 1000kg of a non-conservative contaminant that decays at a first order rate of 0.01/hr. The maximum concentrations were evaluated from: (4-7)

where Cmax is the maximum concentration, M is the mass of pollutant released, t is the travel time for the 10km reach (reach length/area average velocity) and k is the decay rate.

•

20m

• 5m

in-bank - - - - extended in-bank

1.E-04 50

100

150

200

250

300

350

3

Flow Rate (m /s) Figure 4-8. Variation of maximum pollutant concentration with flow rate in three channels.

The results illustrate a number of features that arise from the interaction of three mechanisms that control the pollutant concentration. These are

82

Chapter 4

dilution (determined by flow rate), dispersion (determined by the dispersion coefficient and travel time) and decay (determined by the decay rate and travel time). Some general principles follow that apply to all channels. Firstly, at small flow rates the effect of dilution is low, and the effect of decay is high (because travel times are large). Secondly, at large flow rates the effect of dilution is high, and the effect of decay is low (because travel times are small). In the channels studied here, corresponding principles regarding the effect of dispersion do not exist because of the differing flow dependency of the dispersion coefficient identified earlier. In the in-bank case pollutant concentrations reduce rapidly with increasing flow rate because the effects of dilution and dispersion both increase as flow rate increases and these dominate the decreasing effect of the decay. However, the in-bank case contains the largest pollutant concentrations of all the channels studied. This happens primarily because the flow rates (and hence dilutions) are necessarily small. In addition the dispersion coefficients are also smaller than in the over-bank cases. At low over-bank flows, pollutant concentrations initially increase rapidly with increasing flow rate primarily due to a reduction in the dispersion coefficient, but at high over-bank flows concentrations become approximately constant suggesting that the increased dilution offered by the greater flow rate almost balances the decreased effects of dispersion and decay, both of which reduce as flow rate increases. In the over-bank case the channel with a flood plain width of 20m generally contains pollutant concentrations that are about one order of magnitude smaller than the channel with a flood plain width of 5m. This reduction emanates from both the larger dispersion coefficients and the greater decay caused by the longer travel times. However, the velocity data in Tables 4-3 and 4-4 suggests that the increased dispersion coefficients play the larger role. A further interesting feature of these results is that at similar flows the impact of the pollution incident is smaller in the compound channels than in the extended in-bank (trapezoidal) channel case introduced earlier. This implies that although compound channels are usually designed with flood prevention measures in mind, they also provide advantages for the assimilation of transported pollutants over simpler channel shapes. Indeed, it appears that should it be necessary to discharge some wastewater created by some industrial consequences of a flood event, then a possibly optimum way to do this would be to discharge it to a compound channel when the flow is over-bank but at a relatively small flood plain depth, for example at a flows close to 60 m3/s in the scenario described in Fig. 4-8.

4. Prediction of Dispersion Coefficients in a Compound Channel

7.

83

CONCLUSIONS

This paper describes a theoretical method for evaluating dispersion coefficients in compound channels. The numerical model developed comprises a prediction of the transverse profile of depth-averaged longitudinal velocity followed by the evaluation of a well-known triple integral expression for the dispersion coefficient. Application of the model to in-bank flows yielded dispersion coefficients for a trapezoidal channel that are consistent with other theoretical predictions and which mirror the generally accepted trend of an increasing dispersion coefficient with increasing flow rate. Thus the numerical model is believed to be reliable. Application of the model to over-bank flows has yielded some interesting predictions for the behaviour of dispersion coefficients in such flows. In contrast to the in-bank case, dispersion coefficients decrease with increasing flow rate and are typically two or more orders of magnitude larger. This behaviour is consistent with the development of a strong transverse velocity shear between the deeper and faster moving water in the main channel and the shallower and slower moving water on the flood plains. The flood plain width plays an important role in determining the magnitudes of the dispersion coefficients, with wide flood plains creating much larger dispersion coefficients than narrow ones, because the velocity shear extends over greater length scales. The analysis of the transport of a patch of decaying pollutant along compound and simple channels showed how dilution, dispersion and decay interact to control the maximum concentration over a range of flow rates. These results also suggest that compound channels are more effective at reducing maximum contaminant concentrations than simpler channel shapes carrying similar flow rates, and that under these conditions greater flood plain widths are associated with smaller contaminant concentrations.

ACKNOWLEDGEMENTS The authors would like to thank several of the Workshop contributors for useful discussions of this work.

84

Chapter 4

REFERENCES Babaeyan-Koopaei, K., Ervine, D. A., Carling, P. A., and Cao, Z. X., 2002, Velocity and turbulence measurements for two overbank flow events in River Severn, J. Hydraul Eng., 128:891-900. Deng, Z.-Q., Singh, V. P., and Bengtsson, L., 2001, Longitudinal dispersion coefficient in straight rivers, J. Hydraul Eng., 127:919-927. Deng, Z.-Q., Bengtsson, L., Singh, V. P., and Adrian, D. D., 2002, Longitudinal dispersion coefficient in single-channel streams, J. Hydraul. Eng., 128:901-916. Ervine, D. A., Babaeyan-Koopaei, K., and Sellin, R. H. J., 2000, Two-dimensional solution for straight and meandering overbank flows, J. Hydraul. Eng., 126:653-669. Fischer, H. B., 1967, The mechanics of dispersion in natural streams, J. Hydraul. Div., 93:187-216. Fischer, H. B., 1968, Dispersion predictions in natural streams, J. Sanitary Eng. Div., 94:927-943. Fischer, H. B., 1975, Discussion of Simple method for predicting dispersion in streams by McQuiver R.S. and Keefer T.N., /. Environ. Eng. Div., 101:451-455. Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H., 1979, Mixing in Inland and Coastal Waters, Academic Press. French, R. H., 1986, Open-channel Hydraulics, McGraw-Hill. Jain, S. C , 1976, Longitudinal dispersion coefficients for streams, J. Environ. Eng. Div., 102:465-474. Liu, H., 1977, Predicting dispersion coefficient of streams, J. Environ. Eng. Div., 103:59-69. McQuiver, R. S., and Keefer, T. N., 1974, Simple method for predicting dispersion in streams, /. Environ. Eng. Div., 100:997-110. Rutherford, J. C , 1994, River Mixing, Wiley, Chichester. Seo, I. W., and Cheong, T. S., 1998, Predicting longitudinal dispersion coefficient in natural streams,/. Hydraul. Eng., 124:25-32. Shiono, K., and Knight, D. W., 1991, Turbulent open-channel flows with variable depth across the channel, J. Fluid Mech., 222:17-646. Wallis, S. G. and Manson, J. R., 2004, Methods for predicting dispersion coefficients in rivers, Water Manag., Proc. Inst. Civ. Eng., 157:131-141.

Chapter 5 APPLICATION OF A TRANSIENT STORAGE MODEL TO MEANDERING CHANNEL STUDIES OF SOLUTE TRANSPORT AND DISPERSION Ian Guymer1 and Richard Dutton2 School of Engineering, The University of Warwick, Coventry, UK; 2Department of Civil and Structural Engineering, The University of Sheffield, Sheffield, UK

1.

INTRODUCTION

Practitioners often adopt the Advection Dispersion Equation (ADE) for analysing temporal concentration profiles and predicting the transport and dispersion of solutes in open channel flows. The theory was initially developed for pipe flow by Taylor (1954) and the model predicts instantaneous spatial concentration profiles of Gaussian shape. In a uniform channel, the Fickian molecular model of dispersion may be stated as: dC dC — — ++ v— v— = D— D ot ox ox

(5-1)

where C — average tracer concentration in the cross-section, v = average velocity in the cross-section, D = coefficient of longitudinal dispersion, x = longitudinal distance and t = time. In practice, a simple routing procedure is used to predict the temporal concentration distribution at a downstream site, knowing the temporal concentration at an upstream site (Fischer, 1967, Guymer et al 1999). A stream is a complex heterogeneous environment containing not only free-flowing regions, but also backwater areas, eddies and laminar boundary layers. Observed temporal profiles at fixed locations on a river often appear to have sharper rise times and longer tails than those predicted by the ADE

86

Chapter 5

model (Young and Wallis, 1986). Whilst this may be due to the nature of Eulerian measurements (Chatwin, 1980), the same observed feature is also caused by the trapping and subsequent slow release of the tracer (Valentine and Wood, 1977). A development of a cells-in-series technique, the aggregated dead zone (ADZ) model allows both pure time delay and mixing to take place within a single reach or dead zone element. The ADZ model may be thought of as operating in two distinct phases; linear advection and decay of the upstream profile, followed by exponential decay at the downstream site. The model conceptualises all mechanisms contributing to longitudinal dispersion as 'dead zones', these include boundary layers, vertical and transient shear effects, longitudinal changes in cross-sectional shape and hyphoreic storage. Wallis et al (1989) present a simple discrete-time equation for predicting the temporal concentration profile at a downstream site: C(x2,0 = -aC(x2, f -1) + (1 + a)C(xl 9t-S)

(5-2)

where c{xnt) = concentration at longitudinal position, x. at time t, a = — exp(—Af/77), T= residence time, T = travel time, r =time delay, S = the discrete-time equivalent of the time delay and At = the time step or sampling interval. Transient storage or 'dead' zones cause the temporary detainment of solutes within the body of flowing water. Runkel (1998) describes the two main mechanisms contributing to this storage: • eddies and stagnant pockets of water that are stationary relative to the faster flowing water near to the centre of the channel • significant portions of the flow moving through the porous areas of the streambed and banks A conceptual model has been formed by consideration of two areas: the main channel (portion of stream in which advection and dispersion are the dominant transport mechanisms) and the storage zone (i.e. that which contributes to transient storage). This results in a coupled set of differential equations (Runkel, 1998). This technique has been included in the One Dimensional Transport with Inflow and Storage (OTIS) software produced by the U.S. Geological Survey. Application of these techniques has been the subject of numerous publications. For recent reviews see Schmid (2002), Worman (2000) and Lees et al (2000). An alternative formulation, Hart (1995), has suggested an approach that provides information on the likelihood of the tracer experiencing storage.

5. Application of a Transient Storage Model to Meandering Channel

2.

87

HART (1995) MODEL

The initial differential equations are fundamentally the same as the OTIS model with one equation to solve the solute concentration C[x,t) in the main channel with no lateral inflow and the other for the solute concentration Cs (x,t) in the storage zone.

(5-4) where Q = volumetric flow rate, A = cross-sectional area of the channel, kx = exchange coefficient from the free-flowing water to the storage zone, k2 = exchange coefficient from the storage zone to the free-flowing water. Hart presents the formulation of the simple storage model as a stochastic process, which follows the position of a randomly chosen solute particle that is assumed to move independently of other particles. If the particle has spent a time T in the main channel, its position P is given by Brownian motion with drift: P(T) = VT + W(T)

(5-5)

where v = QIA is the mean stream velocity and W(r) is a Brownian motion with variance 2DT . Whilst in the main channel, the probability of uptake of the particle by the storage zone is described by a Poisson process (with respect to r ) . Once in the storage zone, the probability that the particle returns to the main channel is proportional to the time spent within the zone. Hence, the duration of each visit to the storage zone is defined by an exponential random variable. By considering each of these processes individually, the model can be solved analytically by calculating the probability density function at a downstream detection site, given a constant upstream injection of duration T. The density function is of the form of a rapidly converging series given by:

Chapter 5

o

1 +— " oo T n=\

in t T n

'

0 0

where: vexp\-(x-vt) 1

lr

(5-7)

(5 8

- »

The nth term of the series can be interpreted physically as the concentration of solute at the detection site that has made n trips into the storage zone. Thus, the Hart model provides different information to the OTIS model in that it can be decomposed into its constituent parts allowing information to be inferred such as the distribution of time spent in the storage zone in addition to the predicted concentration.

3,

MODEL VALIDATION AND TESTING

It is essential to test and validate new modelling techniques to confirm not only that computational coding is correct, but also that the results are consistent with observations made from previous model applications. This section concentrates on the application of the Hart (1995) modelling technique to previously published data collected in meandering channels. The analysis has been conducted between temporal concentration profiles collected at various longitudinal locations using both the Hart (1995) model and other modelling techniques. Comparison of the subsequent results will provide evidence of the benefits of transient storage models and also show additional information that can be imparted to suggest greater detail about the longitudinal transport of solutes in impermeable meandering channels. This work is reported in greater detail in Dutton (2004).

5. Application of a Transient Storage Model to Meandering Channel

3.1

89

60 Degree Meandering Channel

Guymer (1998) reports data collected from the Flood Channel Facility at HR Wallingford in the UK, relating to open channel flows within a single planform configuration shown in Fig. 5-1. A smooth mortar screed finish was applied over four complete meander cycles with a crossover angle of 60° and a sinuosity of 1.374. Initial tracer tests were conducted for a channel with constant trapezoidal cross-sectional shape. A second series of tests were undertaken in a channel configuration where the cross-sectional shape varied with longitudinal position throughout the meander cycle (Fig. 5-2). Guymer (1998) refers to this as a "natural" configuration since it was based on an average of field measurement. The bank full cross-sectional area of the 'natural' channel was constant throughout the meander cycle. Details of the velocity distributions within the channel are given in Greenhill and Sellin (1993).

.2 m

x - Flourometer location

Figure 5-1. Plan Geometry and Channel Configuration (Guymer, 1998)

Tracer studies were undertaken at one flow rate on the trapezoidal channel, with a water depth of two thirds that of the section. For the 'natural' channel, tracer studies were undertaken over a range of discharges, from near bank flow conditions (-29 1/s) down to just below the inner bank berm at each apex (-10 1/s). Uniform flow conditions were set and monitored using a series of depth gauges. Short duration pulses of Rhodamine WT dye were introduced as a line source across the bed of the channel inlet through a small diameter pipe with 0.5 mm holes at 5 mm centres. This was done to promote cross-sectional mixing, reducing the distance to well-mixed conditions. Turner Design Series 10 Flourometers in continuous pump through mode were employed to obtain simultaneous measurements of the temporal variation of the solute concentration.

90

Chapter 5 o/s

Section at 0°

I/S

Section at 20°

O/S

I/S

O/S

1024 Section at 40°

Section at 60°

Figure 5-2. Details of Cross-sectional Geometry (Guymer, 1998)

Guymer (1998) presents results of the dispersion coefficient evaluated through calculation of the change in temporal variance of the tracer profiles with distance. This assumes that the mixing processes are constant over the reach, an assumption which can be validated by the quality of the straight line fit obtained. Alternatively, the dispersion coefficient can be evaluated between each pairing of tracer measurement sites, and the consistency of mixing processes over a reach evaluated by calculating the mean and standard deviations of the values obtained. The second method has been adopted in subsequent reanalysis presented by Boxall and Guymer (2004). These values have subsequently been non-dimensionalised with reference to bed shear velocity and hydraulic radius. The ensuing parameters suggest significantly greater values within the 'natural' channel than the trapezoidal cross section. However, this is in spite of the greater transverse secondary circulations with the 'natural' channel, which would tend to reduce the dispersion coefficient (Fischer, 1969). Guymer (1998) suggests therefore, that the trapping mechanisms formed by the longitudinal changes in cross-sectional shape are the more dominant processes. The data sets have been analysed using the ADE, ADZ and Hart methods to produce optimised parameters (Dennis et al, 1999) to better understand the hydraulic processes present within the meandering channel. The results are presented as the average of the mean parameters over the reaches analysed, with error bars representing the mean standard deviations observed from the repeat tests. The 'natural' channel results are taken as average of reaches 2, 3 and 4. The trapezoidal channel results are produced from an average of reaches 1, 2, 3 and 4. The inclusion of a slow response instrument at the apex between reaches 3 and 4 has affected the results from the two

5. Application of a Transient Storage Model to Meandering Channel

91

later reaches but it is thought that the by averaging the results, a corrected parameter set will be obtained. The variation of the mean velocities with discharge has been predicted for all three models for the 'natural' cross-section. The Hart model provides the largest velocities, which are greater than the ADE model, which in turn are larger than the ADZ technique. All three models display a linear trend over the discharge range 17.7 - 28.6 1/s. However, at low flow rates, the models predict velocities below these trends as would be expected due to the increased wetted perimeter and the increased resistance that will be incurred over the berm at the lower water levels. The optimised dispersion coefficients obtained from the Hart and ADE models display a significant reduction in comparison with the non-optimised parameters presented by Guymer (1998) and Boxall and Guymer (2004). The optimised ADE coefficients (Method 3) displayed in Table 5-1 show an average reduction in value of around 40%, as a result of the improved fit to the observed data. Figure 5-3 displays the variation in predicted dispersion coefficient with discharge, for both the optimised ADE and Hart models. This shows an almost linear relationship between dispersion and discharge within the 'natural' channel which was not evident from the non-optimised parameters.

Table 5-1. Comparison of optimised dispersion coefficients with previous studies. Dispersion Coefficients (m2/s) Channel Discharge (1/s) Method 1 Method 2 Method 3 Method 4 0.0592 0.0814 Trapezoidal 46.1 0.0889 0.0683 0.0282 Natural 28.6 0.0892 0.0838 0.0647 21.4 0.1242 0.0902 0.0315 Natural 0.0553 Natural 19.1 0.1198 0.1028 0.0150 0.0479 0.1032 0.0164 Natural 17.7 0.1133 0.0519 0.0125 Natural 13.7 0.0847 0.0759 0.0407 Natural 10.5 0.0663 0.0077 0.0755 0.0308 Method 1 Non-optimised ADE coefficients (Guymer, 1998) Method 2 Non-optimised ADE coefficients (Boxall and Guymer, 2004) Method 3 Optimised ADE coefficients (present study) Method 4 Optimised Hart coefficients (present study)

The Hart dispersion coefficient is on average around 60% smaller than its ADE counterpart in the 'natural' channel, whereas only around 10% smaller in the trapezoidal channel. This suggests that there are greater storage components present within the 'natural' channel, since storage tends to reduce the weighting on the dispersion coefficient to describe the spreading of a solute. This is further supported by the ADZ dispersive fraction results,

92

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which give an indication of the proportion of the reach which contributes to the 'dead zone' effect. Dispersive fraction values in the 'natural' channel show no strong trends with discharge, giving an average value of 0.221 ±0.011. In the trapezoidal channel, the magnitude of the dispersive fraction reduces by 16% to a mean value, at the single flow rate studied, of 0.186.

0.09 0.08 0.07 ^0.06

-•-ADE - Natural -•-Hart-Natural • ADE - Trapezoidal o Hart - Trapezoidal

y

^0.05 |o.O4

L

50.03

T

0.02 0.01 0.00

10

(

/ t

_ ^

Q.

[1

1

1

,

fi ] 20 30 Flow Rate (l/s)

40

50

Figure 5-3. Variation in optimised dispersion coefficients for the ADE and Hart models for the 60° natural and trapezoidal channel data

Further evidence to suggest a reduction in storage within the trapezoidal channel is provided by consideration of the ratio of Hart exchange parameters (ki/k2), which suggests the relative proportions of the conceptual storage zone to the main channel, Fig. 5-4. As discharge increases, there is a slight decrease in the 'natural' channel ratio and also, the ratio observed for the trapezoidal cross-section is almost 60% lower. For predictive purposes it is desirable to attempt to normalise the longitudinal mixing coefficient such that a single dimensionless relationship may be obtained. Guymer (1998) and Boxall and Guymer (2004) both present non-dimensionalised dispersion coefficients, calculated from DIRu*, and observe that it appears to be inversely proportional to discharge, as shown in Fig. 5-5. This leads Boxall and Guymer (2004) to

5. Application of a Transient Storage Model to Meandering Channel

93

conclude that processes other than those accounted for by the parameters used for non-dimensionalising are present. 0.20 0.18

-A-Natural

0.16 0.14

3 0.12

£0.10

A Trapezoidal

fc:

^"0.08 0.06 0.04 0.02 0.00 10

20 30 Flow Rate (l/s)

40

50

Figure 5-4. Optimised Hart predictions for the storage zone to main channel ratios for the 60° natural and trapezoidal channel data.

Table 5-2. Comparison of non-dimensionalised Study Guymer(1998) Boxall & Guymer (2004) Present study (ADE model) Present study (Hart model)

dispersion coefficients. Coefficient, D/Ru* 99.8 ± 20.0 86.2 ±17.3 46.6 ±3.6 17.0 ±5.4

However, application of the same technique to obtain nondimensionalised longitudinal mixing coefficients from the optimised ADE and Hart results, suggests an approximately constant value is obtained with discharge. Figure 5-5 shows that the non-dimensionalised coefficients obtained from the optimised dispersion parameters are significantly lower than suggested by the previous studies. Table 5-2 presents a comparison of the discharge averaged coefficients obtained over the 'natural' channel. It is evident that there is an almost 50% decrease in the coefficient value from the results of Boxall and Guymer (2004) to the present optimised ADE study, due to the use of optimised dispersion coefficients. The standard deviations

94

Chapter 5

have also reduced by around half. The longitudinal dispersion coefficient obtained by the application of the Hart model is also approximately 60% lower than the optimised ADE value, and displays a greater standard deviation.

120 • Natural 1998) • Natural 2004 • Natural ADE) - Natural Hart) • Trapezodal (1998) • Trapezoidal (2004) • Trapezoidal (ADE) A Trapezoidal (Hart)

20 30 Flow Rate (l/s)

40

50

Figure 5-5. Variation of non-dimensional longitudinal mixing coefficientsc for the ADE and Hart models for the 60° channel data

3.2

110 Degree Meandering Channel

The following section concerns the further analysis of a data set from studies undertaken on the Flood Channel Facility at HR Wallingford with a different planform configuration. The channel was of the same type of idealised 'natural', longitudinally variable cross-sectional shape as used for study reported by Guymer (1998). This configuration was based on a 110° meander planform. The channel was cast in concrete and the planform geometry and 3D representation of the bend geometry can be seen in Fig. 5-6. Further details of these planforms and cross-sectional forms can be found in Knight et al (1992).

5. Application of a Transient Storage Model to Meandering Channel

95

-110' Bendi - Flourometer Location

a) Planform Channel Layout, Injection and Monitoring Locations

b) 3D representation of bend geometry Figure 5-6. Details of 110°Meandering Channel Geometry

Tracer studies were undertaken over a range of discharges from bank flow (-25 1/s) down to a minimum cover on the inner berm at each apex of 10mm (-12 1/s) using the same experimental methods and instruments used on the 60 degree channel studies. The instruments were located at the apexes of bends 3, 4, 5, 7 and 8, giving rise to concentration time plots such as that shown in Fig. 5-7.

96

Chapter 5

100

150 200 Time (s)

250

300

Figure 5-7. Typical temporal concentration data set.

4

6

Bend Number

Figure 5-8. Variance of temporal profiles observed at a discharge of 17 1/s.

350

5. Application of a Transient Storage Model to Meandering Channel

97

The data sets used for this analysis are those presented by Guymer and Boxall (2004). In their study the plume edges were defined as a sequence of 30 data points with a concentration of less that 0.1% of the peak. This has resulted in cases where the profiles recorded at the furthest downstream location (bend 8) have been cut-off prematurely. This loss will affect the calculation of the mass balance resulting in corrected downstream profiles that may have peak concentrations in excess of those observed upstream, as seen between the last two profiles in Fig. 5-7. Rutherford (1994) states that in the equilibrium zone the variance should increase linearly as the distance from the source increases. The effect of this process can be seen when considering the variance of the profiles, as shown in Fig. 5-8. The figure shows that the mean variance decreases at the furthest measuring location, indicating that a significant proportion of the tracer has been removed from the profile. This, in turn, will affect the parameters predicted from the optimisation procedures, particularly the coefficients which affect the magnitude of the peak concentration (e.g. dispersion). Therefore, in the subsequent analysis, only the data collected at the first four measuring locations have been included.

0.36 i

0.20

10

12

14

16

18

20

22

24

26

Figure 5-9. Optimised velocity predictions from the ADE, ADZ and Hart models.

The data sets have been analysed using the ADE, ADZ and Hart models. The subsequent results presented concern average parameter values obtained

98

Chapter 5

over the full meander cycles (bend 3 to 5 and 5 to 7). The error bars associated with the averaged parameters refer to the mean standard deviations obtained from the repeat runs over the meander cycles considered. Figure 5-9 shows the trend for the mean velocities predicted over the full meander cycles for all three models. As would be expected, the velocities increase with increasing discharge. Table 5-3 displays the least squares best fit linear equations to the observed data, together with the associated R2 term which measures the goodness of fit. The results show that over this confined range of discharges studied, the velocity variations are approximately linear and the gradients of the best fit lines are very similar.

Table 5-3. Optimised velocity predictions by ADE, ADZ and Hart models. R2 Best Fit Equation ADE 0.9747 v = 0.0046g + 0.217 ADZ 0.9937 v = 0.0047g + 0.1904 Hart v = 0.0047g+ 0.1789 0.9913

Figure 5-10 shows the results of calculation of the optimised longitudinal dispersion coefficient from the measured tracer data.

0.00 10

12

14

16

18 20 Flow Rate (l/s)

22

24

26

Figure 5-10. Optimised longitudinal dispersion coefficient predictions from the ADE and Hart model.

5. Application of a Transient Storage Model to Meandering Channel

99

0.25 i

0.05 10

12

14

16

18 20 Flow Rate (l/s)

22

24

26

Figure 5-11. Optimised dispersive fraction.

The results suggest that the ADE dispersion coefficient is approximately constant at a value of 0.054 ±0.002 m2/s. At low discharges, the Hart dispersion coefficient is approximately 70% lower than the ADE value. This indicates that at low discharges in the 110° configuration, the effects of storage have a significant influence on solute transport, since the weighting on the dispersion coefficient to describe the observed spreading has been reduced. However, the Hart coefficient displays a gradual increase indicating that the effects of the storage zone decreases as the discharge increases. This interpretation is supported by the ADZ dispersive fraction, which gives an indication as to the proportion of the reach which is acting as a 'dead zone' and subsequently detaining solute in the same way as the transient storage concept. Figure 5-11 shows that the dispersive fraction reduces with discharge, suggesting that as the discharge increases, the proportion of the reach contributing to storage declines. Figure 5-12 shows the predicted Hart exchange parameters entering storage over the full meander cycle. The parameter describing exchange into the storage zone, ki, is constant over the range of flows studied at 0.01610.002 s"1. However, the exchange rate out of storage, k2, displays an approximately linear increase, suggesting that as the flow rate increases, the storage zone releases the solute more readily. Figure 5-12 also displays the ratio of exchange parameters (ki/k2) which illustrate the storage area as

100

Chapter 5

a proportion of the main channel area. This ratio tends to reduce as the flow rate increases.

0.00

00

10

12

14

16

18

20

22

24

26

Figure 5-12. Optimised exchange parameters.

90 80 70 60

- Never in Storage -Once -Twice -3 times -4 times -5 times

50 40 30 20 DL

10 0 -10 10

12

14

16

18

20

22

Flow Rate (l/s) Figure 5-13. Proportions of solute experiencing storage.

24

5. Application of a Transient Storage Model to Meandering Channel

101

Figure 5-13 indicates the proportions of solute that the Hart model predicts to enter the storage zone over the full meander cycles, and on how many occasions. This shows that the proportion of tracer never entering storage shows a slight decrease as the flow rate increases over the discharge range 12 to 20 1/s. However, above 20 1/s this shows an increasing trend. Note that this is at the discharge where the gradient of the optimised longitudinal dispersion variation also increases, see Fig. 5-10. This suggests that in these higher flow rates the Hart model assumes the inflow dispersion effects provides the dominant mixing processes, and that solute exchange into the storage zone is reduced.

4,

DISCUSSION

The Hart model has suggested that a storage zone exists within the meander bend. The relative size of this zone varies with discharge, ranging from 13% of the main channel area at a discharge of almost 12 1/s, down to 8% at about 25 1/s. However, it does not suggest where in the cross-section that this zone exists. An initial assumption might be that the storage zone would comprise of the area at the inner bank of the apex over the berm. An additional data set was collected in the 110° meandering channel to investigate the spatial distribution of solute tracer with instruments located at the apex of the bend. One configuration with transverse sampler locations is shown by positions A and C in Fig. 5-14. Two tests were conducted, at flow rates of 15.46 and 24.74 1/s, with the instruments positioned firstly at bends 3 and 7, subsequently at bends 5 and 6. Inspection of the data from the trace with measurements taken at bends 3 and 7 shows that contrary to the expected outcome, the trace at the inner bank arrived before that at the outer bank at both apexes. This indicates a short-circuiting effect around the bend. Analysis of this data gives the difference in the centroids of the tracer clouds at the inner and outer locations for both sets of instrument locations. These were shown to be repeatable at each longitudinal position and were calculated to be 7.16±0.59 s at the high, 24.78 1/s flow rate and 4.41±0.8 s at the lower flow rate of 15.46 1/s. This suggests that the short-circuiting effect is exaggerated as the depth of flow increases. However, since the vertical location of the samplers was not altered between flow rates, the traces are not representative of a proportional depth measurement, and will therefore be subject to the effects of the vertical velocity profile. As the centroid differences are repeatable longitudinally, they were found to be the same at bend 3 and 7,

102

Chapter 5

this suggests that the transverse spreading of the tracer occurs only within the first half of each bend, and is subsequently reversed in the second half, resulting in transverse profiles at the cross-overs which are not skewed. The results of this series of tests suggest that the storage zone is not located over the berm at the inner edge of the bend apex, since the centroids and first arrival times are earlier than those at the outer edge. Therefore, the storage zone must be present elsewhere within the cross-section. An additional series of tests was conducted at the apex of bend 5, with instruments positioned as shown by the letters A to E in Fig. 5-14.

Figure 5-14. Cross-sectional location of samplers.

Inspection of the temporal concentration profiles collected within the cross-section of bend 5 shows how the trace is delayed at the outer edge of the cross-section, but also that there is a vertical trend in the outer section, with a greater retardation of the solute towards the bed of the channel. Analysis of these concentration profiles, Dutton (2004), gives the difference in centroids of the transverse traces relative to those collected at location A (inner edge of cross-section). These are reproduced in Table 5-4. At the lower flow rate the first centroid to arrive is at location B, whereas at the higher flow rate, it arrives first at location A. This indicates that as the flow increases, the short circuiting effect becomes more developed. The centroid at location C is always the last to arrive within the transverse variation, and becomes more delayed as the flow rate increases. Table 5-4 displays the difference in centroids of the vertical traces relative to those collected at location C (top of outer section). In both flow rates the centroid of the trace is most retarded at the lowest point in the cross-section (E). However, as the flow rate increases, this value reduces. Table 5-5 displays the variance of the temporal profiles recorded in the vertical array. There is an increase in variance at deeper locations within the cross-section, with the biggest increase observed between position D and E. This suggests that the profiles are more skewed due to retention of solute at lower depths causing the longer tails in the temporal profiles.

5. Application of a Transient Storage Model to Meandering Channel Table 5-4. Spatial variation in centroid times at one cross-section. Difference in Centroid Times (s) Transverse Vertical Flow Rate (1/s) Location A-B C-D A-C

103

C-E

15.46

Mean SD

-1.93 0.49

1.73 0.55

1.27 0.44

2.96 0.49

24.78

Mean SD

2.30 1.07

6.71 0.97

0.09 0.79

0.95 1.11

Table 5-5. Temporal variance of profiles observed at vertical locations in cross-section. Temporal Variance (s2) E D C Flow Rate (1/s) 15.46

Mean SD

417.33 51.52

423.77 44.03

447.09 23.46

24.78

Mean SD

251.84 38.05

253.01 11.32

285.01 44.51

Table 5-6. Calculation of storage zone depth over range of flow rates in 110° channel. eig te Water Depth* (mm) , 2x (mm ) 141 24.76 90827 22.06 135 83873 20.06 130 78313 16.99 125 72443 15.60 66804 120 13.22 115 61213 55674 110 11.89 *measured from bed of outer section at apex

Flow Rate (1/s)

\L\IV.2 predicted

Mean storage area (mm2)

Resultant depth* (mm)

0.079 0.098 0.114 0.124 0.125 0.128 0.129

6660 7490 7985 8013 7435 6943 6352

49.2 51.4 50.2 52.8 51.2 50.0 48.4

Consideration of temporal profiles recorded at different locations within bend 5, suggests that the region where retardation is at its greatest is towards the bed of the outer section. This is also the location where the profile has the highest variance indicating retention of solute. This suggests that this is where the conceptual storage zone of the Hart model is located. Assuming that the main channel and storage zone are separated by a horizontal plane, and applying the ki/k2 ratio predicted by the Hart model, it is possible to

104

Chapter 5

calculate the thickness of the storage layer. Table 5-6 displays the results of the calculation of this depth over the range of flow rates studied. It is evident that the height of the storage zone (measured from the bed of the outer section of the apex) is independent of discharge with a mean value of 50.5 ±1.47 mm. This implies that the storage layer surface extends nearly to the cross-overs, and is located 50 mm below the berm at the apex of the bend, as shown in Fig. 5-15.

Figure 5-15. Location and extent of storage zone within 110° meandering channel.

Table 5-7. Calculation of storage zone depth over range of flow rates in 60° channel Water Weighted . ., Mean Resultant Channel Flow Rate l 2 Depth* Average , storage height* A Type (1/s) (mm) Area (mm ) area (mm ) (mm) Trapezoidal 46.14 100 100000 0.044 4421 4.9 135 84772 9728 66.9 Natural 28.6 0.115 21.4 Natural 123 70976 0.106 7513 59.6 0.124 8094 Natural 19.1 118 61.6 65313 Natural 115 62.5 17.7 61939 0.135 8371 56.4 Natural 13.7 107 0.124 6585 53030 10.5 Natural 100 45339 51.7 0.116 5281 *measured from bed of outer section at apex

5. Application of a Transient Storage Model to Meandering Channel

105

If it is assumed that the simulated storage zone of the 60° channel (section 3.1) is also located towards the bed of the deeper section, then the same procedure can be applied to this data to calculate the resultant storage zone depth. The results are displayed in Table 5-7. The storage depth for the trapezoidal channel is just less than 5 mm, and is assumed to be constant throughout the meander cycle. The average storage zone depth in the outer section of the apex for the 'natural' 60° channel is 59.8 + 5.3 mm, although there appears to be a slight trend of increasing storage depth with discharge. These results show that there is an increase in the storage depth predicted for the 60° meander in comparison to the 110° channel. This could be attributed to two effects. Firstly, the longitudinal rate of change of crosssectional shape is greater in the 60° meander, resulting in a clearer definition of the boundary of the storage zone and secondly, the greater angle subtended by the 110° channel will allow more secondary circulations to develop within the first half of the bend, in comparison to the 60° configuration. It is anticipated that these secondary circulations will disturb the storage area resulting in an overall reduction in the depth of the zone.

5.

CONCLUSIONS

The transient storage modelling technique developed by Hart (1995) has been applied to temporal concentration profiles collected within impermeable meandering channels. Comparisons have been made with the more commonly used ADE and ADZ equations, and in all cases, as would be expected from a four parameter scheme; the Hart (1995) model has provided a better fit to the observed data. Its application has allowed an improved insight into the processes contributing to the overall longitudinal dispersion. Within the meandering channel results, the impermeable trapezoidal channel provides the lowest storage zone to main channel area ratio. This is due to the constant cross-sectional shape throughout the meander reducing stagnant areas for dead zones to occur. In addition, the high flow rates lead to greater longitudinal velocities, which according to Rozovskii (1957) are directly proportional to the strength of full developed secondary circulation, which will also prevent the formation of storage zones. The ranges of predicted storage area ratio are similar for the 60° and 110° impermeable channels. However, this result may be somewhat misleading, since the 'natural' 60° and 110° channels displayed short-circuiting effects around the inside edge of the apexes. This means that the deeper outer section of the meandering channel acted as dead zones, providing an additional storage capacity. It is suggested that although the cross-section

106

Chapter 5

may be representative of 'natural' meandering channels, the uniform roughness coefficient throughout the cross-section is not. This leads to unrepresentative acceleration of flow at the inner edge of the apex and limits the possible application of the results to natural channels. It does however illustrate a technique that, by application of the Hart (1995) method, has the potential to elucidate the physical processes contributing to longitudinal dispersion in channels exhibiting longitudinal variations in cross-sectional shape.

REFERENCES Boxall, J. B., and Guymer, I., 2004, Longitudinal dispersion in an extreme meander channel with changes in shape, In M., Greco., A., Carravetta, and R., Delia Morte, eds., River Flow 2004 - Proceedings of the Second International Conference on Fluvial Hydraulics, Napoli, Italy, 2:1237-1243. Chatwin, P., 1980, Presentation of longitudinal dispersion data, /. Hydraul Div., 106(l):71-83 Dennis, P., Guymer, I, and Antonopoulos, C , 1999 Optimisation of the Aggregated Dead Zone Model for solute Dispersion in Surcharged Manholes, In Joliffe, I. B., and Ball, J. E., eds., Proceedings of the 8th International Conference on Urban Storm Drainage, Sydney, Australia, 2:763-770. Dutton, R. 2004, Modelling transient storage processes, Thesis presented to the University of Sheffield, Sheffield. Fischer, H. B., 1969, The effects of bends on dispersion in streams, Water Resour. Res., 5(2):496-506. Fischer, H. B., 1967, The mechanics of dispersion in natural streams, J. Hydraul. Div., 93(6): 187-215 Greenhill, R. K., and Sellin, R. H. J., 1993, Development of a simple method to predict discharges in compound meandering channels, Water Marit. Energy, Proc. Inst. Civ. Eng., 101:37-44. Guymer, I., 1998, Longitudinal dispersion in a sinuous channel with changes in shape J. Hydraul. Eng., 124(l):33-40. Guymer, I., Boxall, J., Marion, A., Potter, R., Trevisan, P., Bellinello, M., and Dennis, P., 1999, longitudinal dispersion in a natural formed meandering channel, In Abbott, M. N., et al., eds., Proceedings oflAHR 28th Congress, Graz, Austria. Hart, D. R., 1995, Parameter estimation and stochastic interpretation of the transient storage model for solute transport in streams, Water Resour. Res. 31(2):323-328. Knight, D. W., Yuan, Y. M., and Fares, Y. R., Boundary shear stress in meandering channels, In International Symposium on Hydraulics Research in Nature and Laboratory, Wuhan, China, pp. 102-107. Lees, M. J, Camacho, L. A., and Chapra, S., 2000, On the relationship of transient storage and aggregated dead zone models of longitudinal solute transport in streams, Water Resour. Res. 36(l):213-224. Rosovskii, I. L., 1957, Flow of Water in Bends of Open Channels, Academy of Sciences of Ukranian SSR, (translated by Isreal Prog, for Scientific Translations, Jerusalem, Isreal, 1961).

5. Application of a Transient Storage Model to Meandering Channel

107

Runkel, R. L., 1998, One dimensional transport with inflow and storage (OTIS): A solute transport model for streams and rivers, U.S. Geological Survey Water-Resources Investigation Report 98-4018. Rutherford, J. C , 1994, River Mixing, Wiley, Chichester. Schmid, B. H., 2002, Persistence of skewness in longitudinal dispersion data: Can the dead zone model explain it after all?', J. Hydraul Eng., 128(9):848-854. Taylor, G. I., 1954, The dispersion of matter in turbulent flow through a pipe, Proc. R. Soc. Lond., A, 223:446-468. Valentine, E. M., and Wood, I. R., 1977, Longitudinal dispersion with dead zones, J. Hydraul Eng., 103(9):975-990. Wallis, S. G., Young, P. C , and Beven, K. J., 1989, Experimental investigation of the aggregated dead zone model for longitudinal solute transport in stream channels, Proc.

Inst. Civ.Eng.,Sl(2):\-22. Worman, A., 2000, Comparison of models for transient storage of solutes in small stream, Water Resour. Res., 36(2):455-468. Young, P. C , and S. G., Wallis, 1986, The Aggregated Dead Zone (ADZ) model for dispersion in rivers, In Proceedings of the International Conference on Water Quality Modelling in the Inland Natural Environment, Bournemouth, England.

Chapter 6 EXPERIMENTAL STUDY OF TRAVEL TIMES IN A SMALL STREAM Steve Wallis Heriot-Watt University, Edinburgh, UK

\.

INTRODUCTION

The need to predict the environmental impact of pollution incidents in rivers has spurned the development of several techniques. A great deal of effort has been expended on the development of mathematical models, however, it is also recognized that much can be learned about the response of rivers to the release of pollutants by undertaking controlled tracer experiments. The shape and timing of observed tracer concentration - time profiles, for example, encapsulates the combined effect of all the transport and mixing processes that occur in the reach being studied and hence typifies the response of the system to a pollution incident. At the same time, of course, the availability of tracer data enables the reliability of the mathematical models to be assessed, and when weaknesses are exposed the discrepancies between predicted and observed concentration profiles often indicates where the gaps are in the understanding of, and the representation of, the physical processes. This paper concerns the experimental approach referred to above, and provides some preliminary results from a programme of tracer experiments undertaken on a small stream. The aim of the programme was to provide a good quality data set for (a) studying the solute transport characteristics of the experimental reach and for (b) assessing existing mathematical models. Here, however, the focus is on the former and to satisfy this objective various features of the concentration - time profiles were studied. In particular, the travel times of four key locations on the profiles were

110

Chapter 6

analyzed and the self-similar nature of the profiles was investigated. Some practical applications of the results are also proposed.

2.

EXPERIMENTAL PROGRAMME

The tracer experiments (Burke, 2002) were conducted in a 0.5 km reach of the Murray Burn, which flows through the Heriot-Watt University campus at Riccarton in Edinburgh. Each experiment consisted of the (gulp) injection of a known mass of Rhodamine WT dye at a fixed injection site followed by the measurement of solute concentration-time profiles at up to four fixed sampling sites further downstream. The profiles were obtained by collecting water samples from the central part of the cross-section using a combination of automatic samplers and manual sampling. Tracer concentrations in the water samples were determined under laboratory conditions using a single calibrated Turner Designs fluorometer and allowing for temperature effects. The sampling interval was matched to the flow rate of each experiment, with the aim of capturing well-resolved profiles. An example of the tracer data collected is shown in Fig. 6-1.

40

GO

30

100

Time since injection (min)

Figure 6-1. Illustrative data set from experimental programme.

120

6. Experimental Study of Travel Times

111

A total of 26 experiments were conducted under steady flow conditions during the period February 1999 to April 2000. The experiments were undertaken over stream flows in the range 0 - 3 m3/s, which were independently measured at a calibrated weir immediately downstream of the fourth sampling site. The main features of the experimental reach are summarized in Table 6-1. Table 6-1. Characteristics of the experimental reach. Distance from Mean Length Reach Site width (m) injection site (m) (m) 1 120 3.7 1-2 2 257 137 3.3 356 99 3 2-3 2.4 184 3-4 4 540

3,

Mean slope

Physical description

0.025 0.016 0.009

meandering; boulders straight; cobbles straight; cobbles

SITE TRAVEL TIMES

The transport characteristics of the sites were described in terms of four representative features of the concentration-time profiles. These are the times of travel (measured from the time of tracer injection) of four locations on the concentration-time profile, namely: the leading edge, the peak, the centroid and the trailing edge. The first and last of these were identified as the times when the concentration was 10% of the peak value. Since neither of these two times necessarily coincided with a concentration measurement, linear interpolation between the two measurements either side of the true edges was used to estimate them. The centroid times were calculated using the method of moments.

3.1

Results and discussion

At all sites all four times of travel were found to vary inversely with stream flow, as would be expected. This is illustrated in Fig. 6-2, which shows the centroid travel time data for Site 2. At each site, strong linear correlations were found between the four times of travel such that, for example, the other three could be predicted from the time of the peak with a high degree of confidence. Figure 6-3 shows these relationships, again for Site 2, in which the linear nature of the relationships is particularly striking.

112

3.2

Chapter 6

Applications

Some practical applications of these results are now considered that show how useful information could be extracted from poor quality tracer data that might otherwise be rejected. The case in point is where insufficient sampling has been undertaken as a result of which the tracer profile is incomplete. For example, the tail might be missing because monitoring finished too early, or the rising limb and peak might be missing because monitoring started too late. This can often happen if in-situ tracer measurements are not available in real-time, particularly when tracer experiments are being undertaken in a reach for the first time when only very approximate estimates of travel times are available. Equally, equipment failure or carelessness in transporting samples for later analysis might result in parts of tracer profiles being lost. Figure 6-3 clearly suggests that provided a sufficient number of complete profiles are obtained to define the relationships, then any missing key features of incomplete profiles can be predicted provided one of the other features has been captured. In this regard, the centroid travel time is particularly important because the centroid times of tracer concentration-time profiles at sites are often used to evaluate reach travel times (or velocities) for use in pollution incident and water quality models. As well as their magnitudes, the variation of these reach coefficients with stream flow is required. Yet if the profiles so used are incomplete, the evaluation of the centroid by the method of moments (the usual approach) is subject to error. The commonest case is where the peak has been captured but the trailing edge is incomplete. In such cases, however, Fig. 6-3 suggests that knowledge of the peak-centroid travel time relationship would allow the centroid travel time to be estimated with some confidence. This would enlarge the data set available for identifying the stream flow dependence of the reach coefficients and, in particular, would reduce the uncertainty in any predictions made from this dependency at extreme flows. Other cases of incomplete profiles could be catered for in similar ways. It is interesting to speculate how many incomplete profiles may have been rejected in previous experimental studies that could, in fact, have yielded useful information.

6. Experimental Study of Travel Times

113

5000

Flew(m3/s)

Figure 6-2. Illustrative relationship between centroid travel time and flow.

8000

6000

•

Leading edge

•

Centroid

A

Trailing edge

4

- - • Linear (Leading edge) - — Linear (Centroid)

4000

— 'Linear (Trailing edge)

2000

500

1000

1500

2000

2500

3000

3500

Peak travel time(s)

Figure 6-3. Illustrative relationships between travel times.

4000

4500

114

Chapter 6

4.

SELF-SIMILARITY OF TRACER PROFILES

An inference from the strong relationships found between the four times of travel is that at each site the tracer profiles are self-similar in shape over the range of flows studied. This concept was introduced by Day and Wood (1976) and considered by Sukhodolov et al (1997), but otherwise seems to have been ignored by workers during the last twenty-five years. To investigate this, therefore, each tracer concentration profile was normalized with respect to concentration and time. The former entailed division by the peak concentration: the latter entailed scaling the time according to the time delay between the leading and trailing edges. The procedure is described by the following equations. Cn~

(6-1)

(6 2>

-

Here, Cn is the normalized concentration, C is the observed concentration, Cp is the observed peak concentration, tn is the normalized time, t is the observed time, ti is the observed travel time of the leading edge and tt is the observed travel time of the trailing edge.

4.1

Results and discussion

An illustrative set of results is shown in Fig. 6-4, where excellent selfsimilarity is demonstrated by the collapse of the data on to a single normalized profile. Bearing in mind that the individual observed profiles were collected over a wide range of flows, it is clear that the normalized profile is independent of flow rate. In theory, all the normalized profiles pass through the non-dimensional co-ordinates of (0, 0.1) and (1, 0.1) because the leading and trailing edges are defined as the times when the concentration is 10% of the peak value. In practice, there are some small discrepancies from this because the times of the leading and trailing edges were not known precisely, being derived via linear interpolation (as described earlier).

6. Experimental Study of Travel Times

OJO

0.5

115

1J0

1,5

2.0

2.5

Normalized time

Figure 6-4. Normalized concentration - time curves for Site 4.

4.2

Applications

Two practical applications of the self-similar profiles are now considered. Note that in these applications a set of mean normalized time and concentration co-ordinates were derived for each site from each family of self-similar profiles, such as that shown in Fig. 6-4. Firstly, the profiles can be used to fill in any gaps in observed profiles, see for example Fig. 6-5. Here the observed profile has a missing tail. The restored profile is complete, however, and the excellent agreement with the part of the observed profile that does exist indicates that the prediction of its missing tail is reliably provided. In this example, the construction of the restored profile requires the following steps: • • •

predict the trailing edge travel time from the peak travel time; predict concentrations from Eq. (6-1) using normalized concentration coordinates and the observed peak value; predict times from Eq. (6-2) using corresponding normalized time coordinates, the observed leading edge travel time and the predicted trailing edge travel time.

In the spirit of the earlier applications discussed in Section 3, this provides a useful way of enhancing the value of poor quality tracer profiles, making them more useful, for example, in calibration exercises of

116

Chapter 6

mathematical models such as the advection-dispersion equation (Fischer et al, 1979; Rutherford, 1994) or the aggregated dead zone model (Wallis et al, 1989;Wallis, 1993).

1.2

1.0

0.8

0.6

§

0.4

0.2

0.0

• Observed profile — Restored profile

,'V

50 100 Time since injection (min)

150

Figure 6-5. Illustrative restoration of an incomplete observed profile.

Secondly, the self-similar profiles can be used in their own right as the basis for modeling solute transport in rivers, as described below. In this, rather than rely on a mathematical representation of the transport processes, it is recognized that the normalized tracer profile for a site contains most of the information required to predict the passage of a pollutant past the site. Indeed, the normalized tracer profile is simply a form of response function that describes how a discretely released mass of solute becomes dispersed as it travels between the release site and the observation site. The real power of this idea for the Murray Burn data lies in the fact that the response function is remarkably independent of stream flow. The prediction of a concentration profile requires four pieces of information: • • • •

the flow rate at which the prediction is required; the normalized concentration - time profile for the site at which the prediction is required; the travel time features for the site at which the prediction is required; an estimate of the peak concentration at the site at which the prediction is required.

6. Experimental Study of Travel Times

117

The first of these is a free choice whilst the second and third are provided by a few preliminary tracer experiments in the reach of interest. The fourth can also be estimated from this data by using the concept of the Unit Peak Attenuation (UPA) curve.

10

20

30

40 SO t i m e of Peak (min)

Figure 6-6. Illustrative example of a UPA curve.

This follows from work in the USA, see for example Kilpatrick and Taylor (1986) and Jobson (1997). In the UPA approach the analysis of tracer experiment data suggests that a relationship exists between the time of the peak concentration, tp, and a normalized measure of the peak concentration itself, known as the unit peak concentration, Cup. A unit concentration is simply the concentration that would be observed if lkg of solute entered a stream that was flowing at a rate of Im3/s. An observed concentration, C, is converted to its unit form, Cu, using the following equation:

c = MR u

A

(6-3)

118

Chapter 6

Here Q is the flow rate, M is the mass of solute that entered the stream, R is the solute recovery ratio (mass recovered/M) and A is the area under the concentration - time profile. The UPA curve for Site 2 is shown in Fig. 6-6 and illustrates the welldefined trend that is typical of UPA curves. Note that, for convenience, the unit peak concentrations in Fig. 6-6 have been multiplied by 100. The construction of a predicted concentration - time profile at a site requires the following steps: • • • • • •

select the flow, Q, for which the prediction is required; obtain the time of the peak, tp, from the tp - Q curve for the site of interest; obtain Cup from the UPA curve for the site of interest; obtain Cp from Cup using Eq. (6-3); obtain the time of the leading, ti, and trailing, tt, edges from tp; obtain concentrations and times from the co-ordinates of the normalized concentration - time profile for the site of interest using Cp, ti and tt.

1.4

10

g0.8 S 0-6 §

• data prediction - - prediction (observed peaks)

isx

1.2

- ft'

- Ill

0.4

0.2

0.0 "—

i 20

40

60

80

100

120

Time since injection (minutes)

Figure 6-7. Prediction of tracer profile using normalized concentration - time curves.

The results of a prediction at Site 2 are shown in Fig. 6-7. Clearly, there is a phase error and the peak is under-predicted, otherwise the prediction is

6. Experimental Study of Travel Times

119

quite good. The source of these discrepancies lies in the second and third steps in the procedure, i.e. in the prediction of the peak. If the time and magnitude of the observed peak are used instead of those for the predicted peak, better agreement with the observed data is found (see Fig. 6-7). Further work with this method of solute transport modeling is required before its merits can be fully assessed. In particular, reducing the error in the prediction of the peak and comparing predicted concentration - time profiles with those derived from traditional modeling approaches.

5.

CONCLUSIONS

The analysis of solute concentration - time profiles from a series of tracer experiments in a small stream have revealed a number of interesting concepts, and some practical applications of these have been illustrated. The two main findings are: •

•

the travel times of key locations on the concentration - time profiles are well correlated with other: this enables useful information to be extracted from incomplete profiles that otherwise might be rejected from further analysis. the concentration - time profiles at a site are self-similar over a wide range of flows so that when expressed in non-dimensional form they collapse on to a single profile: this enables incomplete profiles to be restored and provides, in its own right, a method for modeling solute transport in rivers.

REFERENCES Burke, N. A., 2002, Travel time and flow characteristics of a small stream system, Ph.D. thesis, Heriot-Watt University, Edinburgh. Day, T. J., and Wood, I. R., 1976, Similarity of the mean motion of fluid particles dispersing in a natural channel, Water Resour. Res., 12:655-666. Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H., 1979, Mixing in Inland and Coastal Waters, Academic Press, New York. Jobson, H. E., 1997, Predicting travel time and dispersion in rivers and streams, J. Hydraul. Eng.9123:971-978. Kilpatrick, F. A., and Taylor, K. R., 1986, Generalization and applications of tracer dispersion data, Water Resour. Bull., 22:537-548. Rutherford, J. C , 1994, River Mixing, Wiley, Chichester. Sukhodolov, A. N., Nikora, V. I., Rowinski, P. M , and Czernuszenko, W., 1997, A case study of longitudinal dispersion in small lowland rivers, Water Resour. Res., 69:1246-1253.

120

Chapter 6

Wallis, S. G., 1993, Aggregated mixing zone modeling of solute transport in rivers, In Proceedings of the 4th National Hydrology Symposium, BHS, Cardiff, UK, pp. 5.9-5.13. Wallis S. G., Young, P. C , and Beven, K. J., 1989, Experimental investigation of the aggregated dead zone model for longitudinal transport in stream channels, Proc. Inst. Civ. Eng.9 87(2): 1-22.

Chapter 7 MIGRATION OF FLOATING PARTICLES IN A COMPOUND CHANNEL Pawel M. Rowinski1, Wlodzimierz Czernuszenko1 and Marcin Krukowski2 1

Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland; Agriculture University, Warsaw, Poland

\.

2

Warsaw

INTRODUCTION

Rivers during flood are characterized by a compound cross-section (water overflows the banks to floodplains) and therefore understanding of the mechanisms governing the transport of various constituents in two-stage channels is a challenging task within environmental hydraulics. It has been recognized that the shear layer generated by the difference in velocities in the main channel and in the floodplains influences the turbulence structure and as a consequence it should impact on the transport of mass in a two-stage channel (Knight and Shiono, 1990; Knight et al., 1994; Shiono and Knight, 1991; Rowinski et al., 2002, Sofialdis and Prinos, 1999). From that studies it turns out that the intensity of turbulence increases significantly at the interface between shallow and deep areas of the channel as well as horizontal vortices develop in this area. Researchers have realized that studies of the mixing processes in channels of irregular cross-section are of great importance, however most of the attempts have been based on numerical investigations (e.g. Nokes and Hughes, 1994; Shiono et al., 2003). Experimental investigations in this respect are still lacking. Among the best-known are the studies of Wood and Liang (1989) and recently of Shiono and Feng (2003) who simultaneously measured the tracer concentrations and the flow characteristics in a compound channel. The mentioned studies are all based on the traditional Eulerian approach and they consist in the measuring of the breakthrough curves at selected cross-sections.

122

Chapter 7

The present paper pertains to the studies of the transport of test particles in a Lagrangian frame in the compound channel flows. A number of the floating particles were released into a turbulent flow in a way allowing to trace them with video cameras. Obviously because the turbulent velocity fluctuations are irregular, the results of each trail differ. On average the particles wander apart from each other and the rate at which they wander apart can be related to the diffusion coefficient. A few similar experiments were made in the past but only in regular experimental channels, see for example Iwasa and Aya (1985), Czernuszenko (1983), Orlob (1959). Experimental investigations of that kind in a compound channel are discussed in this paper in details. Surface floats obviously tend to overestimate the depth-averaged transverse dispersion coefficients, but they offer a convenient tool for their estimates (Rutherford, 1994) and for gaining the basic understanding of the spread of admixture in geometrically complex open channels. Some authors even argue that one may obtain the same results from the surface velocity measurements using Particle Image Velocimetry as from the "depth-averaged" dye tracer tests (Kurzke et al., 2002). It is also worth mentioning that a variety of visual methods have been recently promoted also in case of compound channels. A good example is the work of Bousmar and Zech (2002) who investigated the turbulent structures in a compound channel with the use of specially designed Particle-Tracking Velocimetry (PTV). It is well-known that the concentration of a substance transferred by a turbulent flow exhibits a complex, chaotically evolving structure over a broad range of space and time scales and as such is still far from full understanding. Shraiman and Siggia (2000) in their recent study published by Nature pointed the necessity to decouple what is called "passive scalar" turbulence from those of the underlying velocity field. Despite new elaborated techniques of so called multi-point correlators it seems that the researchers are still at the very beginning of understanding of those complex systems. The overall aim of this report is to present a simple empirical approach allowing for the study of the trajectories of floating particles in a compound channel. A relatively modest technique allowed us only for the "old fashion" method of analysis concentrated on two-point statistics and its scaling and on snapshots of the velocity and scalar field and the identification of spatial and temporary structures.

7. Migration of Floating Particles in a Compound Channel

2.

123

AN OUTLINE OF THE THEORETICAL BACKGROUND

A particle placed in homogeneous turbulence responds to the random fluid velocity and as a result its motion undergoes random displacements that are defined by turbulence structure and by interaction between particle and turbulence. The writers fully realize that the detailed description of the movement of solid particles calls for the use of the equation of motion of a particle for example in version proposed by Tchen (see e.g., Hinze 1975). In principle we will deal with very small particles and very low particles concentrations, then the base flow is not affected by the presence of the particles - a circumstance known as "one-way coupling" (Elghobashi, 1994). It is simply assumed that the particle displacement is a direct result of the water turbulence. Very crude estimates of particles' velocities due to further equipment limitations cause that all those detailed considerations do not make sense. Therefore we shall interpret the experiment results on migration particle based on traditional turbulent diffusion theory formulated analogously to Taylor (1921) who introduced his concept to a study related to the spread of heat and soluble matter. We assume that Fick's law is valid, so that particles are in local equilibrium with the surrounding fluid so the diffusion equation can be applied. For homogenous turbulence such condition implies that the particle relaxation time must be much greater than the integral time scale of turbulence and much less than the particle diffusion time (Mols and Oliemans, 1998). Then the motion of particles is statistically similar to Brownian motion. The analysis of movement of small particles will be performed by means of the Lagrangian method, which is typical in the turbulent diffusion approach. Let's assume that a solid particle that is not distinguished from fluid particle is introduced to the turbulent flow at time t0 = 0 and that the particle is carried along with the Eulerian water velocity, u(X, t). Denoting the displacement of the chosen particle x at time t = x by X(x, T), one can write

X(x,r) = JV(x,0*

(7-1)

where X = (Xu X2, X3) are Eulerian coordinates of the vector point, also these coordinates are denoted by (X, Y, Z); x = X(x, t0) is the Lagrangian coordinate of a fluid particle at moment to = 0, X(x, t) is the random vector of displacement of particle x, V(x, t) is the Lagrangian particle velocity

124

Chapter 7

vector represented with the Eulerian velocity vector by formula: V(x,t) = u(X(x,t),t). Vector of displacement is a random value and its determination requires the knowledge of the three dimensional probability density p(X 1t, x, t0) of the position of the selected particle x in the neighbourhood of X at time t. As mentioned before we will further consider the case of stationary and homogeneous turbulence. In such case it can be shown that the probability density function (PDF) of the fluid particle position p(X | x, t) is Gaussian. Let's consider two major characteristics of the random vector of displacement, i.e., its first and second moments. The mean value of this vector is represented by

X(JC,T)=

j\(x9t)dt

(7-2)

and its turbulent fluctuation t

Xf(x,0 = X(x,0-X(x,f)= \v\x9s)ds

(7-3)

whereas the tensor of second moments of the random displacement can be presented in the form (see Monin and Yaglom, 1971) 0.5

(7-4)

The tensor of second moments (TSM) depends on time and also on the shape of the correlation function Ry(t) which in a certain sense is a measure of the memory of the flow, i.e. how well correlated future velocities are with the current value. It would be expected that the shape of the autocorrelation function Rn(t) would tend to zero for long times and it is approaching one when time comes to zero. The time scale for this process is defined by: (7-5)

It is known as the Lagrangian or diffusion-integral time scale of the flow, and it gives rise to a definition of a Lagrangian or diffusion-integral length scale in the form:

7. Migration of Floating Particles in a Compound Channel 1

125 (7-6)

The time scale TL is usually considered as a measure of the longest time during which on the average a particle persists in a motion in a given direction. The length scale LL is closely related to the largest eddies occurring in homogenous turbulent flow (Roberts and Webster, 2002). The smallest eddies existing in turbulent flow are characterised by length and time scale (Kolmogorov microscale), respectively il = ( v 3 / e ) l / \

2.1

x-(v/s) 1 / 2

(7-7)

Estimation of turbulent diffusion coefficients

The autocorrelation function Rii(t) is equal to unity for the initial time and its value tends to zero for long times. For both very short times and very long times the main components of the tensor of second moments may be substantially simplified to two following forms: for times much shorter than the Lagrangian macroscale, TjL DH(t) = Z*t2

(7-8)

and for the other extreme when t » TjL Du{f)^2^tTtt

(7-9)

Relationship (7-4) is the most important result of Taylor's theory and it indicates the linear dependence between variance and time for the particle long travel time (see Eq. 7-9). Recalling that such feature is characteristic for molecular diffusion one concludes that for long times an analogy between turbulent and molecular diffusion exists. In other words Eq. (7-9) states that after elapsing of a sufficiently long time, the variance of the particle cloud increases linearly with time at a rate given by 2ut aTt. The given rate is the property of the turbulent flow field and not the fluid as in the case of molecular diffusion. The above mentioned sufficiently long time means that we need to wait until the motion of each particle is not correlated with its initial motion. Equation (7-9) may be treated as a measure of spread of the solute cloud released from a fixed point source in the turbulent flow, i.e., D^ are variances of the concentration distribution of solute in the cloud and they are denoted

126

Chapter 7

here as Oi2. The product ut values is presented in Table 8-7 and Fig. 8-10. These results show again, that primarily natural dead zones in combination with morphological variations along the river causes the measured persistence of the skewness in rivers.

Table 8-7. Optimised mass-transfer coefficient k, tracer experiments 03/94 (River Aare) and the corresponding coefficient of proportionality OCy of the transverse dispersion coefficient after Eq.(8-20). River Section Aare-km (upstream end) Length k Oy (km) (10-V) (-) 32 185.6 48.6 6.0 234.2 12.8 3.9 29 3.2 247.0 22 15.8 262.8 5.8 20 2.9 268.6 2.9 20 2.8 6.0 2.8 271.5 19 277.5 10.1 18 2.5 2.8 2.3 287.6 17 290.4 14 2.8 9.3 6.8 13 2.9 299.7

8. Persistence ofSkewness of Concentration Distributions

163

Tracer experiment 03/94 (R. Aare) Skewness coeff. Gt & Mass-transfer coeff. k dead-zone parameter R =0.03

- 1.0E-03

2-, 1.61.2® 080.4n 190

1 nc_rvi

210

230

250

270

290

310

Aare-km Theor. appr.

•

Measured

A

Mass-transfer coeff.

Figure 8-10. Evaluation of the skewness coefficient, tracer experiment 03/94 (River Aare) without artificial dead zones; optimised mass-transfer coefficient distribution A: with J3= 0.03.

Since there are no artificial dead zones like groyne fields in the River Aare, the optimised mass-transfer coefficient k should be more or less equal ktrans defined by Eqs. (8-19) and (8-20): =

ktmns=Dy/(0.5B)2

(8-23)

Thus, the coefficient of proportionality Oy in Eq. (8-20) can be given by: ^ _ftC,(0.5i?) 2

(8-24)

The resulting c^-values are also presented in Table 8-7. The average value is about 3 with an exceptional large value of 6 for the first river reach of 48.6 km. This indicates a very good transversal mixing and consequently a small longitudinal dispersion, which is in accordance with the applied (and calibrated) values of the longitudinal dispersion coefficient D after the Rhine Alarm-Model. Considering the longitudinal dispersion coefficient after Fischer etal. (1979): (8-25)

164

Chapter 8

the coefficient of proportionality a* for the River Aare is significant smaller (about 0.002) than for the River Rhine (about 0.01). (Spreafico and Mazijk, 1996; Neff et al., 1996a). The large 6^-values might be explained by two aspects: (1) sharp bends as there are just downstream of the Lake of Biel, generating significant secondary circulation (Rutherford, 1994, pp. 108-113) and (2) canalisation due to the construction of lateral channels with power stations, which result into less difference in longitudinal advection over the cross section of the river.

4.3

River Mosel

The evaluation of the skewness coefficient in the River Mosel concerns the river reach from Mosel-km 103 to 1.941. According to the schematisation of the River Mosel within the Rhine Alarm-Model, the section breaks are chosen at the locations of the weirs: St. Aldegund (Mosel-km 78.3), Fankel (Mosel-km 59.38), Miiden (Mosel-km 37.1) and Lehmen (Mosel-km 20.84). The applied mean flow velocity U and longitudinal dispersion coefficient D are derived from the hydrological data of the Rhine Alarm-Model. As discussed for the River Aare the fitting of the measured distribution of the skewness coefficient Gt in the River Mosel has also been executed visually by optimising the ^-values, assuming a natural dead-zone parameter value of 0.03. In Table 8-8 the optimised mass-transfer coefficients are presented.

Table 8-8. The optimised mass-transfer coefficient k, tracer experiments 11/92 (River Mosel) and the corresponding coefficient of proportionality (Xy of the transverse dispersion coefficient after Eq. (8-20). River Section Mosel-km (upstream end) k Length (km) (lO'V1) 1.9 103.00 40.0 24.70 1.3 78.30 18.92 27.0 59.38 22.28 25.0 1.2 37.10 23.9 16.26 1.1 20.84 21.7 18.90 1.0

1

The number of kilometres along the River Mosel starts at the confluence with the River Rhine at Koblenz and counts in upstream direction.

8. Persistence of Skewness of Concentration Distributions

165

Tracer experiment 11/92 (R. Mosel) Skewness coeff. Gt & Mass-transfer coeff. k dead zone parameter R = 0.03 1.0E-03

T

1.0E-04 90 80 70 60 50 40 30 20 10 0 Mosel-km •Theor. appr. -Mass-transfer coeff.

•

Measured

Figure 8-11. Evaluation of the skewness coefficient, tracer experiment 11/92 (River Mosel) without artificial dead zones; optimised mass-transfer coefficient distribution A; with /?= 0.03.

Since in the River Mosel there are no artificial dead zones like groyne fields, again the optimised mass-transfer coefficient k can be equated with the transverse mixing coefficient ktram. The resulting devalues after Eq. (8-24) are listed in Table 8-8 with an average value of about 1.2. Again this value is larger than 0.65, as applied for the River Rhine, but in accordance with the applied (and calibrated) values of the longitudinal dispersion coefficient D for the River Mosel with a* = 0.007 instead of 0.01 as found for the River Rhine. Also in this case the small c^-value might be explained by sharp bends in the river between Enkirch and Koblenz generating secondary circulation as well as the canalisation of the River Mosel, reducing the difference of the longitudinal advection over the cross section of the river.

5.

CONCLUSIONS

The approximation of the limb of measured concentration distributions by an exponential description avoids inaccuracies arising by background concentrations, influences of second waves due to lateral canals with different travel times or missing and inaccurate data. The derived skewness

166

Chapter 8

coefficients Gt from the measured concentration distributions show the persistence of the skewness along the River Rhine as well as along the tributaries Aare and Mosel. The skewness coefficient along the River Rhine and the tributary Mosel is approximately 1, whereas the coefficient along the River Aare persists at a level of about 0.5. These results confirm the applicability of the Hermite polynomial in the Rhine Alarm-Model after Eq. (8-18) (see also Mazijk, 2002) with a skewness coefficient equal 1 in order to represent the skewness of the concentration distributions of spills in the River Rhine. For the River Aare the Grvalue of about 0.5 means that the Rhine Alarm-Model predicts a longer passage time at a certain location. This is still acceptable, since the released amount of pollutant is mostly known approximately and therefore the predicted concentration-values indicative, whereas in practice sampling controls the water quality during the passage of accidental spills. By applying the theoretical approach of Schmid (2002) the measured distribution of the skewness coefficient in the River Rhine and its tributaries Aare and Mosel can be reproduced properly and explains the persistence of skewness in particular. For this reproduction a dead zone of a few percent of the cross-sectional area of the river has to be assumed in river reaches without artificial dead zones. Small regions along the bottom and riversides, where the flow is nearly stagnant, explain the existence of these 'natural' dead zones. The positive result of the data fitting of the distribution of the skewness coefficient by applying Schmid's (2002) approach also shows that the persistence of the skewness is caused by tributaries, confluences of lateral river branches, significant morphological variations and so on. For the reproduction of the distribution of the skewness, the masstransfer coefficient k has been optimised with values ranging from 6-10"4 s'1 to 10"5 s"1. Although the tributaries do not have artificial dead zones like groyne fields, this range covers the ranges found for these rivers (Tables 8-7 and 8-8). Along the River Rhine this coefficient shows a decreasing tendency with the distance from the point of release of the tracer. Comparison of these values with the time scale of transverse mixing processes and exchange processes between the main stream and artificial dead zones like groyne fields, shows the predominance of the transverse mixing in the main stream, regarding the influence of the mass-transfer between the dead zone and the main stream on the skewness of concentration distributions. It has to be stressed that this conclusion refers to the River Rhine with a relative large width-depth ratio. For the tributaries Aare and Mosel without artificial dead zones the optimised mass-transfer coefficient k might represent to a certain extent the transverse dispersion coefficient. Thus the ^-values, found by fitting the measured distribution of the skewness coefficient Gh result into a first

8. Persistence ofSkewness of Concentration Distributions

167

indication of the coefficient of proportionality Oy of the transverse dispersion coefficient. The achieved values of 3 for the River Aare and 1.2 for the River Mosel show a significant larger transversal mixing in these tributaries than in the River Rhine (0.65), which corresponds with the smaller values of the calibrated longitudinal dispersion coefficients in these rivers. To which extent this is caused by the existing sharp bends with significant secondary circulation and/or the canalisation of these rivers should be the aim of further research. The use of the optimisation function FMINSEARCH of MATLAB® was restricted by the fact that the number of the parameters to be optimised (mass-transfer coefficients) was slightly less than the data to be fitted (skewness coefficients).

REFERENCES Czernuszenko, W., and Rowinski, P. M., 1997, Properties of the dead-zone model of longitudinal dispersion in rivers, J. Hydraul Res., 35(4):491-504. Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J., and Brooks, N. H., 1979, Mixing in Inland and Coastal Waters, Academic press, New York, pp. 112-117. Mazijk, A., van, Verwoerdt, P., and Mierlo, J., van, 1991a, Calibration of the Rhine Alarm-Model, based on the tracer experiments 04/89, Village Neuf - Netherlands (in German), Delft University of Technology, Faculty of Civil Engineering, and Ministry of Transport, Public Works and Watermanagement, Institute for Inland Water Management and Waste Water Treatment, Lelystad, March 1991. Mazijk, A., van, Mierlo, J., van, and Wiesner, H., 1991b, Validation of the Rhine AlarmModel, Version 2.0 (in German), Delft University of Technology, Faculty of Civil Engineering, and Albert-Ludwigs-University Freiburg, Institute of Physical Geography, June 1991. Mazijk, A., van, Mierlo, J. C. M., van, Wiesner, H., and Leibundgut, Ch., 1992, Validation of the Rhine Alarm-Model, based on the tracer experiments 06/91 and 07/91 (in German), Delft University of Technology, Faculty of Civil Engineering, and Albert-LudwigsUniversity Freiburg, Institute of Physical Geography, Dec. 1992. Mazijk, A., van, and Mierlo, J. C. M., van, 1992, Checking of the calibration of the Rhine Alarm-Model, Version 2.1, based on the tracer experiment 04/89 Village Neuf Netherlands (in German), Delft University of Technology, Faculty of Civil Engineering, and Albert-Ludwigs-University Freiburg, Institute of Physical Geography, Dec. 1992. Mazijk, A., van, 1996, One-dimensional approach of transport phenomena of dissolved matter in rivers, Dissertation, Delft 1996; also published in: Communications on Hydraulic and Geotechnical Engineering, Report Nr.96-3, Delft University of Technology, Faculty of Civil Engineering, September 1996. Mazijk, A., van, 2002, Modelling the effects of groyne fields on the transport of dissolved matter within the Rhine Alarm-Model, J. HydroL, 264:213-229. Neff, H.-P., Leibundgut, Ch., and Mazijk, A., van, 1996a, Calibration of the Rhine AlarmModel for the River Aare, based on the tracer experiment 03/94 (in German), Report 57 of the Chair for Hydrology, Albert-Ludwigs-University Freiburg, February 1996.

168

Chapter 8

Neff, H.-P., Leibundgut, Ch., and Mazijk, A., van, 1996b, Calibration of the Rhine AlarmModel for the River Mosel, based on the tracer experiment 11/92 (in German), Report 58 of the Chair for Hydrology, Albert-Ludwigs-University Freiburg, February 1996. Nordin, C. F., and Troutman, B. M , 1980, Longitudinal dispersion in rivers: the persistence of skewness in observed data, Water Resour. ites. 16(1): 123-128. Rutherford, J. C , 1994, River Mixing, Wiley, Chichester, pp. 108-113. Schmid, B. H., 2002, Persistence of skewness in longitudinal dispersion data: Can the dead zone model explain it after all?, J. Hydraul Eng., 128(9):848-854. Spreafico, M., and Mazijk, A., van, ed., 1993, Alarm model Rhine, A model for the operational prediction of the transport of pollutants in the River Rhine (in German), IRC/CHR Committee of experts, report Nr. 1-12 of the CHR, Secretariat CHR, Lelystad, ISBN 90-70980-18-5. Valentine, E.M., and Wood, I.R., 1977, Longitudinal dispersion with dead zones, J. Hydraul. Div., 103(9):975-990. Weitbrecht, V, and Jirka, G. H., 2001, Flow Patterns and Exchange processes in dead zones of Rivers, In Li, G., ed., Proceedings oflAHR 29th Congress, Beijing, China, technical session B, pp. 439-445. Yotsukura, N., Fischer, H. B., and Sayre, W. W., 1970, Measurements of mixing characteristics of the Missouri River between Sioux City, Iowa and Plattsmouth, Nebraska, Water-Supply Paper 1899-G, U.S. Geological Survey.

Chapter 9 MOMENTS AND ANALYTICAL SOLUTION OF COUPLED EQUATION DESCRIBING TRANSPORT OF POLLUTANTS IN RIVERS Ed J. M. Veling Delft University of Technology, Faculty of Civil Engineering and Geosciences, Water Resources Section, Delft, The Netherlands

1.

INTRODUCTION

A number of authors (among others Nordin and Troutman, 1980; Schmid, 1995, 2002, 2003; Czernuszenko and Rowinski, 1997a; Worman, 2000; Seo and Cheong, 2001) have studied the transport of solutes along rivers in terms of the moments. Under a number of simplyfing assumptions the relative simple equations they studied are given by

dt

dx2

dt

T

(9-1)

°° , since the numerator is linear in x and the denominator is proportional to x3n . See also the discussion by Schmid (1997b) and Czernuszenko and Rowinski (1997b).

4.

ANALYTICAL SOLUTION INITIAL VALUE PROBLEM

In this section we shall solve the problem defined by the Eqs. (9-1), (9-2), (9-3) and (9-4). The solution technique (see Walker, 1987) we use allows can be applied to a broad class of equations of the type by changing Eq. (9-1) into (9-49) where the operator L represents any second-order differential expression in x. In Section 1 the form of the operator L was ^2r dx

dC ^ dx.

(9-50)

We assume that we know the solution of the uncoupled problem, that is nW

— = Lw, w(x,0) = o(x), -°°b /A is modeled as follows:

^Q>h =-^j{CL -{c))-a{Cs

-(C»

(11-10)

where As [L2] is the cross sectional area of the storage zone; qL [^T1] is the lateral volumetric flow rate per unit length; a [T]] is the stream storage exchange coefficient; Cs [ML3] is the solute concentration in the storage zone. If the lateral flow qL is negligible (or CL = ) the flux of contaminant across the bed surface is proportional to the difference of concentration between the water column and the pore water in a bed layer of constant depth, assuming a uniform pore water concentration in the storage bed layer, Cs(t). The Transient Storage Model has been applied to a large number of streams, principally to evaluate metal transport in mining areas and the influence of hyporheic exchange on nutrient transport (Triska et al., 1989, 1990, 1993; Hart 1995; Winter et al, 1998; Wagner and Harvey, 1997; Packman and Bencala, 2000). The TSM is a very useful tool for practical analysis of stream-subsurface exchange. However, it does not fully represent the physics of the pumping process, where advective flows are produced by the pressure gradients at the bed surface associated with the presence of geometrical irregularities. Marion et al. (2003) showed that the two calibration parameters employed by TSM, As and a, are not to be considered as constants for a given stream. They change with the time scale of the contamination process and depend also on the shape of the breakthrough

11. Models ofHyporheic Contamination

221

curve in the stream. They proposed an appropriate scaling of the parameters based on the stream geometry and on the properties of the porous boundary: kA

aOH kKh

(11-12)

B

where K [LT1] is the hydraulic conductivity of the sediments, k [L1] is the bedform wavenumber, equal to ITIIX (k is the bedform wavelength), hm [L] is the amplitude of the pressure head on the bed surface, 6 is the sediment porosity, H [L] is the effective water depth in the main channel and B [L] is the channel width. The dimensionless quantities in Eq. (11-12) are derived from comparison with the Advective Pumping Model discussed in section 3.3. They provided a tool for the estimate of a* and 8* as a function of the timescale of the process, for a few fundamental shapes of the pollutograph, i.e. of the stream concentration. An example is shown in Fig. 11-1. Zaramella et al. (2003) showed that the TSM is still applicable with constant parameters with shallow beds that have a defined exchange layer restricted by the presence of an impermeable boundary. In this case, transient storage parameters can be directly related to the streamflow conditions and the channel geometry. The TSM is not as efficient in representing exchange with a relatively deep sediment bed, where flow along different advective paths in the bed yields a wide distribution of exchange timescales.

- normalized exchange rate • normalized RMS

10 T*

100

1000

Figure 11-1. Variation of the dimensionless parameters (solid curves) of the TSM with the contamination timescale, for a step-change of the in-stream concentration. Dashed curves show values of the dimensionless rms error S*. (Marion et al., 2003).

222 3.2

Chapter 11

Diffusive model (DM)

The flux Ob can be modelled as a Fickian diffusive term, assuming that the flux of solutes within the hyporheic zone is proportional to the vertical gradient of concentration in the sediments. Thus the mass transfer at the stream-subsurface interface is proportional to the gradient of concentration evaluated at the bed surface, z=0, z being the vertical coordinate:

dy

(11-13) z=0

where Ds [L2T!] is the diffusion coefficient within the sediments, assumed constant throughout the depth, and Cs is the concentration in the bed expressed as a function of z. The model that couples Eq. (11-9) and Eq. (11-13) can be applied for natural streams (Jackman et al., 1984). The diffusion coefficient, Ds, had to be evaluated up to now by model calibration using field data, since its theoretical evaluation was not yet available. Zhou and Mendoza (1993) theorized that the hyporheic exchange with flat gravel beds depends on turbulent interactions between the flowing water and the sediments surface. Packman et al. (2004) linked the diffusion coefficient to the Reynolds number, analyzing experimental data obtained with flat beds. This is in agreement with the idea that turbulence-induced mass transfer across the flow/bed interface dominates in the case of flat beds.

- normalized diffusion coefficient • normalized RMS

-

TTTT|

1 I llllll|

10 T*

1 I llllll|

100

1X102

S*

1 I Illlllj

1000

10000

Figure 11-2. Variation of the dimensionless diffusion coefficient with the contamination timescale for a step change of concentration (Marion and Zaramella, 2004).

11. Models ofHyporheic Contamination

223

When bedform-induced flow in the porous medium is observed, the diffusion coefficient should be scaled with the pressure head of the perturbation, with the bed porosity and permeability, leading to the following dimensionless coefficient (Marion and Zaramella, 2004): (11-14)

OKh'm

The assumption of a constant diffusive coefficient over all times is not physically based as for the case of the parameters of the TSM. In the case of a step-change of concentration, the dimensionless diffusion coefficient shows a strong dependence from the timescale of the process as shown in Fig. 11-2.

3.3

Advective Pumping Model (APM)

Elliott and Brooks (1997ab) modelled the flux mechanism due to the presence of stationary bedforms. Experiments with passive substances have shown that solutes are transported into the bed by the flow field generated by the induced dynamic head on the bed surface. Bedform-induced pumping has been determined solving analytically the subsurface flow field for a bed of semi-infinite depth. The flow field is assumed to be generated by a sinusoidal distribution of dynamic pressure at the bed surface. This model uses a dimensionless expression for time and for the penetrated mass of passive solutes into the bed: . Ink m m* =

e c0

** =

k2Khm -t

(11-15)

e

where m [ML2] is the mass per unit area, penetrated into the bed, given by the integral of Ob over time, Co [ML3] is a reference concentration in the mean flow and hm[L] here is the half-amplitude of the sinusoidal distribution of pressure on the bed surface. The dimensionless mass of pollutant entering the bed, expressed by Eq. (11-15), is given by the convolution integral of the residence time function and the normalized concentration C* = C/Co: jr(T*)C*(t*-T*)dT*

(11-16)

224

Chapter 11

where, q* = q/OKkhm with q [LT1] is the average water flux per unit length and unit width towards the sediments. The residence time function F is defined as the probability of a particle that entered the bed at time t = 0 to be in the bed at time t. Evaluation of the function F(t) and q* can be derived by direct resolution of the flow paths within the bed. An expression of the flux 0b in Eq. (11-9) according to the APM has been proposed by Worman et al. (2002). It is demonstrated that the APM yields a good prediction of the hyporheic exchange induced by bedforms for passive solutes (Elliott and Brooks, 1997b) and reactive solutes like metals (Eylers et al., 1995) and colloids (Ren and Packman, 2002).

4.

APPLICATION TO METALS

Ionic solutes like metals often show sorption properties when they are in contact with river bed sediments. The equilibrium quantity of reversibly adsorbed tracer can be expressed using the retardation coefficient R. This coefficient represents the inverse fraction of tracer per unit volume remaining in solution in the pore water. R is given by the expression: R = l + ^kp

(11-17)

where kp[L3/M] is the partition coefficient. The partition coefficient kp represents the ratio between the number of moles adsorbed per unit sediment mass and the moles contained within a unit volume of solution. Thus, if Cs is the concentration of metals in the pore water, this time a function of position, then kpCs is the mass of tracer adsorbed per unit mass of sediments: Cads=kpCs

(11-18)

The concentration of ions at the water-grain interface is assumed to reach equilibrium instantly. The streamline transport equation in porous media of adsorbing solutes, neglecting dispersion phenomena, is written as: (1M

+ US

dt

s

ds

e

dt

where us [LT1] is the mean water velocity within the porous media.

9)

11. Models ofHyporheic Contamination

225

Using Eq. (11-17) and Eq. (11-18), Eq. (11-19) becomes: R ^ +u s ^ =0 at d

(11-20)

which has the same expression of the transport model for passive solutes, except for the presence of the retardation coefficient, that appears as a factor of time t. Equation (11-20) is valid under the hypothesis of instant reaction, i.e. when the time scales of adsorption kinetics are small compared to the timescales of the flow through the porous medium. Thus the formulation of the TSM applied to instantly reactive solutes is:

0,-20 Analysis of the TSM theories applied to reactive solutes can be derived in analogy with passive solutes formulation. The analysis of field cases (Bencala 1983, 1984) shows that the in-stream concentration of metals strictly depends on the quantity adsorbed by the bed sediments. This phenomenon is due to the retention of reactive solutes within the sediments. Experimental results with highly variable retardation factors, obtained using zinc adsorbing onto silica sand at various pH (Eylers et al., 1995), show that the water column is washed by metal contaminants depending on the sediments adsorption strength and on the volume of water running above the sediments. Zaramella et al. (2004) showed evidence of strong parameter variability in the TSM over the time range for which the fitting computation is made, but the dimensionless time includes the retardation coefficient, so that just one fitting curve is found even though the sorption coefficient, kp, varies. Thus Fig. 11-1, relative to the case of step-change concentration, can be extended to reactive solutes by normalizing the dimensionless time with the retardation coefficient. APM theory relative to passive solutes has been extended to the case of adsorbing solutes, evaluating the ionic retention into the bed sediments synthesized by the retardation coefficient R. The residence time function for sorbing solutes corresponds to the residence time function for passive solutes, where the time is scaled with the retardation coefficient (Eylers etal., 1995), as Eq. (11-21) directly suggests. Thus the expression of the residence time function for sorbing solute is rads(t) = rpass(t/R), where rpass(t) is the residence time function for passive solutes.

226

Chapter 11

5.

APPLICATION TO COLLOIDS

Colloids are small particles subject to a significant gravitational effect due to their weight. Gravity induces particle settling with a velocity v dependent on particle geometry and on fluid properties. Colloids are trappeds by sediments grains during the filtration processes. It is known that a fraction of the suspended particles are retained in the small pores that are present on the grains surface: the captured part of colloid is proportional to the path covered during filtration in the small channels created by pores. Then the steady-state concentration of suspended colloid in a solution moving into the pore water decreases with the law: ^

= -AfCs

(11-22)

where Xf [L'1] is the filtration coefficient, and s [L] is the coordinate along particles path. Despite of the property to be sensitive to gravity forces, colloidal particles may behave like a solute in the stream water, where turbulence is generally strong enough to keep particles acting as wash load. However, when particles enter the sediment pores, their behaviour has to be analysed case by case. The case where colloids are fully retained within the sediment matrix has been modelled by Zaramella et al. (2004). While colloidal particles are often highly mobile in the stream flow, within the streambed they can be readily removed from suspension due to a combination of settling and filtration (Ren and Packman, 2002). One important limiting case is where the rate of particle removal from pore water flow is very high so that all particles that enter the bed are deposited. This situation has been termed "complete trapping" (Packman et al., 2000a, 2000b) and it corresponds to a constant residence time function F(t) = 1, leading to: (11-23)

The TSM can correctly represent a pumping process that implies the storage of tracer without release only if the storage zone has an infinite depth. In this case, the exchange rate is equal to the net flux entering in the sediments, and colloid trapping can be represented in the TSM only using the following parameters: a* = ?*

£*_>oo

(11-24)

11. Models ofHyporheic Contamination

227

Then when complete trapping occurs an infinite depth of the storage zone offers the best approximation for the process of colloid penetration. The set of parameters reported in Eq. (11-24) shows that transient storage parameter may lose physical sense when applied to fully filtered particles.

6.

FUTURE RESEARCH OBJECTIVES

The understanding and the prediction of the behavior of rivers with respect to the propagation and retention of pollutants entering the water body accidentally or from controlled sources has been based up to now mainly on the determination of diffusion and dispersion parameters through direct measurements, such as tracer tests. However, tracer tests can be executed only under a few flow stages of the river, usually avoiding periods of high discharge or flooding. Therefore, understanding the physical processes governing the transport of pollutants and developing mathematical models is necessary to identify correct calibration parameters from tracer tests, to predict the behaviour of a river under discharge conditions that are different from those in which the tracer tests were carried out and to scale such parameters to different rivers. Current research has developed models capable of simulating some but not all of the mechanisms responsible of hyporheic fluxes in natural rivers. The ongoing discussion has identified a variety of mechanisms acting at different time and spatial scales. The observation that advection driven by pressure gradients due to hydrodynamic effects developing at the interface between the flow and permeable boundaries dominates the long-term retention of pollutants provides a reference for future models. Writing mass balance equations averaged over appropriate temporal and spatial scales is expected to lead to the development of models for hyporheic flux induced by i) sediment heterogeneities such as the presence of layered sediment deposits with composition and permeability gradients (Giuliani, 2003); ii) geometrical irregularities, such as alternate bars, meanders and width variations; iii) unsteady flows, such as short floods and flushing operation. Results from the research on hyporheic exchange may aid the modelling of water quality not only in natural water bodies but also in artificial environments, such as sewers. Some recent work (Tait et al., 2003) has highlighted the role of oxygen and bacteria transfer across the flow/bed interface on the consolidation of deposits with significant organic content. Studies on hyporheic contamination have led to well over a hundred papers in major scientific journals in the last decade, and are certainly expected to grow and broaden in the years to come.

228

Chapter 11

ACKNOWLEDGMENTS The work reports recent findings achieved by the author through collaborations with highly appreciated colleagues like Vladimir Nikora, Aaron Packman, Ian Guymer and Mattia Zaramella. The work has been funded by the Italian National Research Council, Group on the Defence from Chemical and Industrial Hazards (GNDCRIE) and by the Italian Ministry of the Environment, project on "An Integrated Approach to the Remediation of Polluted River Sediments".

REFERENCES Bencala, K. E., and Walters, R.A., 1983, Simulation of solute transport in a mountain pooland-riffle stream: a transient storage model, Water Resour. Res., 19:718-724. Bencala, K. E., 1983, Simulation of solute transport in a mountain pool-and-riffle stream with a kinetic mass transfer model for sorption, Water Resour. Res., 19(3):718-724. Bencala, K. E., 1984, Interactions of solutes and streambed, 2. A dynamic analysis of coupled hydrologic and chemical processes that determine solute transport, Water Resour. Res., 20(12):1804-1814. Bencala, K. E., Kennedy, V. C , Zellweger, G. W., Jackman, A. P., and Avanzino, R. J., 1984, Interactions of solutes and streambed sediment, 1. An experimental analysis of cation and anion transport in a mountain stream, Water Resour. Res., 20:1797-1803. Bencala, K. E., 1993, A perspective on stream-catchment conditions, J. N. Am. Benthol. Soc, 12(l):44-47. Castro, N. M., and Hornberger, G. M., 1991, Surface-subsurface interactions in an alluviated mountain stream channel, Water Resour. Res., 27(7): 1613-1621. Coleman, M. J., and Hynes, H. B. N., 1970, The vertical distribution of the invertebrate fauna in the bed of a stream, Limnol Oceanogr., 15:31-30. Elder, J. W., 1959, The dispersion of marked fluid in turbulent shear flow, J. Fluid Mech., 5:544-560. Elliott, A. H., Brooks, N. H., 1997a, Transfer of nonsorbing solutes to a streambed with bed forms: theory, Water Resour. Res., 33(1):123-136. Elliott, A. H., and Brooks, N. H., 1997b, Transfer of nonsorbing solutes to a streambed with bed forms: laboratory experiments, Water Resour. Res., 33(1): 137-151. Eylers, H., Brooks, N. H., and Morgan, J. J., 1995, Transport of adsorbing metals from stream water to a stationary sand-bed in a laboratory flume, Mar. Freshw. Res., 46:209-214. Fernald, A. G., Wigington, Jr. P. J., and Dixon, H. L., 2001, Transient storage and hyporheic flow along the Willamette River, Oregon: field measurements and model estimates, Water Resour. Res., 37(6): 1681-1694. Fischer H. B., List, E. J., Koh, R. C. Y., Imberger, J., Brooks, N. H., 1979, Mixing in Inland and Coastal Waters, Academic Press, San Diego. Giuliani, D., 2003, Experimental observations of hyporheic transport in case of armoured or stratified streambed, Laurea thesis, University of Padua, Padua. Hart, D. R., 1995, Parameter estimation and stochastic interpretation of the transient storage model for solute transport in streams, Water Resour. Res., 31(2):323-328.

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Harvey, J. W., Wagner, B. J., and Bencala, K. E., 1996, Evaluating the reliability of the stream tracer approach to characterize stream-subsurface water exchange, Water Resour. Res., 32(8):2441-2451. Harvey, J. W., and Fuller, C. C , 1998, Effect of enhanced manganese oxidation in the hyporheic zone on basin-scale geochemical mass balance, Water Resour. Res., 34(4):623-636. Hynes, H. B. N., 1974, Further studies on the distribution of stream animals within the substratum, Limnol. Oceanogr., 19(l):92-99.Jackman, A. P., Walters, R. A., and Kennedy, V. C , 1984, Transport and concentration controls for chloride, strontium, potassium and lead in Uvas Creek, a small cobble-bed stream in Santa Clara county, California, /. Hydrol, 75:111-141. Marion, A., Bellinello, M., Guymer, I., and Packman, A. I., 2002, Effect of bed form geometry on the penetration of passive solutes into a stream bed, Water Resour. Res., 38(10):1209. Marion, A., Zaramella, M., and Packman, A. I., 2003, Parameter estimation of the Transient Storage Model for stream-subsurface exchange, J. Environ. Eng., 129(5):456-463. Marion, A., and Zaramella, M., 2004, On the diffusive behaviour of bedform-induced hyporheic exchange in rivers, (submitted). Nikora, V., Goring, D., McEwan, I. K., and Griffiths, G., 2001, Spatially averaged open-channel flow over rough bed, J. Hydraul Eng., 127(2): 123-133. Mulholland, P. J., Marzolf, E. R., Webster, J. R., Hart, D. R., and Hendricks, S. P., 1997, Evidence that hyporheic zones increase hetrotrophic metabolism and phosphorus uptake in forest streams. Limnol. Oceanogr., 42:443-451. O'Connor, D. J., 1988, Models of sorptive toxic substances in freshwater systems, III: Streams and rivers, J. Environ. Eng., 114(3),552-574. Packman, A. I., Brooks, N. H., and Morgan, J. J., 2000a, A physicochemical model for colloid exchange between a stream and a sand streambed with bed forms, Water Resour. 7tes.,36(8):2351-2361. Packman, A. I., Brooks, N. H., and Morgan, J. J., 2000b, Kaolinite exchange between a stream and stream bed: Laboratory experiments and evaluation of a colloid transport model, Water Resour. Res., 36(8):2363-2372. Packman, A. I., and Bencala, K. E., 2000, Modeling surface-subsurface hydrological interactions, In Jones, J. B., and Mulholland, P. J., eds., Streams and Ground Waters, Academic Press, San Diego, pp. 45-80. Packman, A. I., Salehin, M., and Zaramella, M., 2004, Hyporheic exchange with gravel beds: basic hydrodynamic interactions and bedform-induced advective flows, J. Hydraul. Eng., 130(7). Ren, J., and Packman, A. I., 2002, Effects of particle size and background water composition on stream-subsurface exchange of colloids, J. Environ. Eng., 128(7):624-634. Richardson, C. P., and Parr, A. D., 1988, Modified fickian model for solute uptake by runoff, J. Environ. Eng., 114(4):792-809. Runkel, R. L., and Chapra, S. C , 1993, An efficient numerical solution of the transient storage equations for solute transport in small streams, Water Resour. Res., 29(1 ):211-215. Runkel, R. L., Bencala, K. E., Broshears, R. E., and Chapra, S.C., 1996a, Reactive solute transport in streams, 1. Development of an equilibrium based model, Water Resour. Res., 32(2):409-418. Runkel, R. L., McKnight, D. M., Bencala, K. E., and Chapra, S. C , 1996b, Reactive solute transport in streams, 2. Simulation of a pH modification experiment, Water Resour. Res., 32(2):419-430.

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Runkel, R. L., Kimball, B. A., McKnight, D. M., and Bencala, K. E., 1999, Reactive solute transport in streams: a surface complexation approach for trace metal sorption, Water Resour. Res., 35(12):3829-3840. Rutherford, J. C , Latimer, G. J., and Smith, R. K., 1993, Bedform mobility and benthic oxygen uptake, Water Resour. Res., 27(10):1545-1558. Rutherford, J. C , Boyle, J. D., Elliott, A. H., Hatherell, T. V. J., and Chiu, T. W., 1995, Modeling benthic oxygen uptake by pumping, J. Environ. Eng., 121(1):84-95. Savant, S. A., Reible, D. D., and Thibodeax, L. J., 1987, Convective transport within stable river sediments, Water Resour. Res., 23(9): 1763-1768. Stanford, J. A., and Gaufin, J. V., 1974, Hyporheic communities of two Montana rivers, Science, 185(8):700-702. Stanford, J. A., and Ward, J. V., 1988, The hyporheic habitat of river ecosystems, Nature, 335(l):64-66. Tait, S. J., Marion, A., and Camuffo, G., 2003, Effect of environmental conditions on the erosional resistance of cohesive sediment deposits in sewers, Water Sci. Technol, 47(4):27-34. Taylor, G. I., 1954, The dispersion of matter in turbulent flow through a pipe, Proc. R. Soc. Lond., A, 223:446-468. Triska, F. J., Kennedy, V. C , Avanzino, R. J., Zellweger, G. W., and Bencala, K. E., 1989, Retention and transport of nutrients in a third-order stream in northwestern California: Hyporheic process, Ecology, 70(6): 1893-1905. Triska, F. J., Duff, J. H., and Avanzino, R. J., 1990, Influence of exchange flow between the channel and hyporheic zone on nitrate production in a small mountain stream, Can. J. Fish. Aquat. Sci., 47:2099-2111. Triska, F. J., Duff, J. H., and Avanzino, R. J., 1993, The role of water exchange between a stream channel and its hyporheic zone in nitrogen cycling at the terrestrial-acquatic interface, Hydrobiologia, 251(13): 167-184. Vallet, H. M., Morice, J. A., Dahm, C. N., and Campana, M. E., 1996, Parent lithology, surface-groundwater exchange, and nitrate retention in headwater streams. Limnol. Oceanogr., 41(29):333-345. Wagner, B. J., and Harvey, J. W., 1997, Experimental design for esitmating parameters of rate-limited mass-transfer: Analysis of stream tracer studies, Water Resour. Res., 33(7):1731-1741. Winter, T. C , Harvey, J. W., Franke, O. H., and Alley, W. M., 1998, Ground water and surface water: A single resource, USGS Circular 1139, Denver. Worman, A., 2000, Comparison of models for transient storage of solutes in small streams, Water Resour. Res., 36(2):455-468. Worman, A., Forsman, J., and Johansson, H., 1998, Modelling retention of sorbing solutes in streams based on a tracer experiment using 51Cr, J. Environ. Eng., 124(2): 122-130. Worman, A., Packman, A. I., Johansson, H., and Jonsson, K., 2002, Effect of flow-induced exchange in hyporheic zones on longitudinal transport of solutes in streams and rivers, Water Resour. Res., 38(1):15. Zaramella, M., Packman, A. I., and Marion, A., 2003, Application of the Transient Storage Model to analyze advective hyporheic exchange with deep and shallow sediment beds, Water Resour. Res., 39(7): 1 lp. Zaramella, M., Marion, A., and Packman, A. I., 2004, Analysis of the hyporheic exchange of metals and colloids with the Transient Storage Model, (submitted). Zhou, D., and Mendoza, C , 1993, Flow through porous bed of turbulent stream, J. Eng. Mech., 119(2):365-383.

Chapter 12 THE FLOW IN GROYNE FIELDS Patterns and Exchange Processes Wim S. J. Uijttewaal Environmental Fluid Mechanics section, Delft University of Technology The Netherlands

1.

INTRODUCTION

In many European rivers groynes are used for the stabilisation of the banks. In general groynes are built as spur dikes almost perpendicular to the bank. A lot of variation is found in the exact lay out of the spur dike (Przedwojski et al., 1995; Nakel, 1970). In lowland rivers that have a natural tendency to be wide and shallow and to exhibit a dynamic meandering behaviour groynes are very efficient. With limited costs the river stream is confined and the main channel is deepened creating a navigation channel. This successful application has resulted in thousands of groyne structures in the greater parts of the large European rivers like the River Rhine and the River Elbe. The European groyne design has also been transferred from the Netherlands to Japan more than two centuries ago. A by-product of groynes is the area between the groynes, the groyne fields. Here the flow is virtually stagnant and has a permanent open connection with the main stream. Hence there is a continuous exchange of mass and momentum with the main stream. In this exchange process dissolved and suspended matter will enter the groyne field and remain there for a certain time. For a solute it will be the retention time associated with the mean circulation. For sediment, algae and fish larvae the specific properties of the turbulent motion together with settling velocity or active locomotion determine the location and duration of residence (Brinke et al., 1999; Schwartz and Kozerski, 2003). With the presence of groynes also the variability in flow properties is increased (Arlinghaus et al, 2002).

232

Chapter 12

When considering water quality in relation with the spill and transport of pollutants the role of groyne fields is important from various viewpoints. 1. Groyne fields act as dead-zones and therefore have a retarding effect on the transport velocity and the dispersion of a pollutant cloud. 2. The flow velocities in the groyne field are small which can result in the settling of suspended particles to which contaminants can be attached. Accumulation of pollutants in groyne fields will make these areas a problem for river management. 3. The flow conditions in a groyne field can be beneficial for certain biological species. The ecological richness of groyne fields is in itself a quality that requires special attention when water quality is a concern. It is important to have a detailed view of the circulation in groyne fields not only for the dispersion behaviour of a pollution spill but also for the long term water quality and ecological development (Ockenfeld and Guhr, 2003). It is obvious that the design of the groyne shape and the orientation of the groyne with respect to the flow is governing the flow pattern and exchange parameters. With design parameters like length, inclination, spacing, height, permeability a number of flow features can be influenced (United nations, 1953; Richardson et al, 1975). The retention time, flow velocities and turbulence properties can in principle be adjusted with respect to the quality (ecology, conveyance capacity, navigation) that receives priority for a given river reach. In this chapter, research on the hydrodynamics in groyne fields will be summarised. First, an overview will be given of the results of previous research on flow patterns in the whole groyne field. Second, a more detailed analysis will be presented on the flow patterns in the area around a groyne tip. Finally, attention will be paid to the relevance of laboratory experiments for the flow on a prototype scale.

2.

FLOW PATTERNS

2.1

Whole groyne field

Bank protection by mean of groynes is established by keeping the high flow velocities in a river away from the bank. Blocking the flow in the near-bank region confines the cross-sectional area which leads to higher velocities in the centre of the river with a consequent deepening of the main channel. This provides a second purpose for groynes. The equilibrium bed level in the main channel can be 'tuned' locally by choosing the proper length for the groynes.

12. The Flow in Groyne Fields

233

The standard flow field in groyne field of aspect ratio close to unity consists of a single gyre that fills up the whole groyne field (Fig. 12-1). The circulation is driven by the momentum exchange through the mixing layer.

Mixing layer —• Figure 12-1. Patterns as observed with dye exchange experiment for two different aspect ratios w/1 = 0.7 left, w/1 = 0.3 right.

In the corners near the bank small counter rotating gyres are found. With this geometry a stable circulation is obtained which flows rather smoothly at about 30% of the main stream velocity. When the distance between the groynes increases to an aspect ratio of about 3, the circulation cell becomes elongated and separates from the bank (see also Chen and Ikeda, 1997; Kimura and Hosoda, 1997; Uijttewaal et al., 2001; Weitbrecht and Jirka, 2001). This provides room for a secondary gyre rotating in the opposite direction. The secondary gyre gets its momentum from the primary gyre via an intermediate mixing layer resulting in a velocity of approximately 30% of the speed of the primary gyre. There appears to be no direct contact between the secondary gyre and the main stream. Its flow velocity and the exchange with the main stream are therefore very small. The mixing layer is on average wider than in the square groyne field. It starts already with a significant width and grows further downstream over the length of the groyne field. This is due to the vortex shedding that occurs at the groyne tip and the velocity gradient sustaining the vortical motion. Due to the dynamics in the flow in the mixing layer the instantaneous velocity field differs considerably from the time averaged flow pattern. This is nicely visualised in the comparison in Fig. 12-2. The primary and secondary gyre look smooth and well defined in the time averaged picture. This pattern can hardly be recognised from the instantaneous picture where a vortex detaches from the groyne tip and merges with the primary gyre. The

234

Chapter 12

strong deformation of the gyre pattern and the large contribution of the dynamic eddy to the exchange of mass and momentum gives an impression of the difficulties associated with the forecasting of mixing and transport. The dominant length scale of horizontal mixing is intermittently governed by the dynamic eddy that does not show up in the mean flow field. Moreover, on the downstream side of the groyne tip a scour hole is formed which is often associated with the dynamics of the flow in that area Garde et al. (1961), Gill (1972).

Sec

1

Dynamic Eddy

Prim |

ill

[.•:•:•.

. .r r JL JL .1 J!'- .IT,LIJUL i T

i*\

• Figure 12-2. Difference between time averaged and instantaneous flow field (Uijttewaal et al.,2001).

In the same experiment the background of the vector plot shows a dye visualisation of the associated exchange of mass. Starting with a groyne field homogeneously coloured the exchange of mass gradually washes out the dye, first from the primary gyre, later on also from the slower exchanging secondary gyre. The figure also shows the important role played by the dynamic eddy in this process. Figure 12-3 shows the decrease in time of the dye content as measured in the two different groyne fields of Fig. 12-1. The logarithmic scale for the concentration make the exponential decay visible as a straight line. This holds for more than 90 percent of the rapid exchange of the large groyne field while the smaller groyne field shows a gradual deviation from this line starting beyond 50 percent. Although the exponential decay can be associated with a first order process where the decrease in concentration is proportional to the concentration itself, the visualization of this process (Fig 12-1) shows that the dynamics of this exchange are quite complicated. Nevertheless it appears correct to assume a single retention or relaxation time in modeling the

235

12. The Flow in Groyne Fields

exchange (Altai and Chu, 1997; Uijttewaal et al., 2001; Weitbrecht and Jirka, 2001).

0.01

400

Figure 12-3. Decay of an initial homogeneous concentration distribution for groyne fields of different aspect ratios (Uijttewaal et. al., 2001).

With the exchange process characterized by a single parameter the effect of groyne fields on the dispersion in rivers can easily be represented in a one-dimensional model (Mazijk, 2002). For practical applications this requires detailed information of the groyne field geometries for a certain river reach (Weitbrecht et al., 2004).

Prim

Dynamic area

Penetration of main stream Figure 12-4. Time average flow pattern in groyne field with aspect ratio W/L = 0.167.

By increasing the distance between the groynes further the flow pattern in the downstream side of the groyne field changes while in the upstream part the primary and secondary gyre remain qualitatively the same (Chen and Ikeda, 1997). At the location where the main stream brings highmomentum fluid into the groyne field a slowly varying flow field is

236

Chapter 12

observed yielding an elongated recirculation area in the time averaged vector field labelled in Fig. 12-4 as a dynamic area. Instantaneously the bank is exposed to the high velocities of the main stream. With an even larger spacing between the groynes the main stream will re-attach to the bank. In principle this could be at a spacing of the order of the reattachment length downstream of a sudden widening which is about 8 times the groyne length (Babarutsi and Chu, 1989). Provided the shallowness in the groyne field and the associated influence of bed friction as well as the curvatures found in the main stream the distance should be taken significantly shorter. Ideally speaking the main stream should not penetrate significantly into the groyne field. This would locally lead to a decreased velocity in the main channel and the risk of the formation of a sand bank. Also the attack on the downstream groyne will be larger when the high- momentum stream hits the stagnation point. In practice the optimal groyne spacing is found between one and three times the groyne length.

Bank

Main stream

Bank

Main stream

Figure 12-5. Sketch of flow patterns in groyne fields with different groyne inclination, pointing downstream (left), and upstream (right), (adapted from Weitbrecht 2004).

In addition to the groyne spacing the inclination of the groyne with respect to the bank affects the flow pattern (Fig. 12-5). The upstream pointing groynes do deflect the large velocities away from the bank at certain stages of submergence, as opposed to the downstream pointing groynes. The scour hole formed near the tip of the groyne is located further away from the bank with the upstream pointing groyne as opposed to the downward pointing one (Kuhnle et al., 2002). Therefore the latter type has the connotation of a flow-attracting groyne and is applied less frequently. The exchange of mass with such groynes is significantly smaller (Weitbrecht, 2004). An interesting modification to inclined groynes is found in so called kinked groynes (see Fig. 12-6). The part of the groyne closest to the main

12. The Flow in Groyne Fields

237

stream is oriented downstream (Henning, 2000). This results in a groyne field with little exchange under normal flow conditions, while at high water levels the flow over the groynes establishes a good exchange with the main channel. The strong variations in the flow conditions in the groyne field provide an environment with clear ecological advantages (Hentschel and Anlauf, 2002).

Figure 12-6. Groyne design optimized for ecological purposes (Hentschel and Anlauf, 2002).

2.2

The flow around the groyne tip

Up to this point the groynes have been considered as relatively simple impermeable straight dikes. Depending on the required flow conditions and the available construction material an infinite number of geometries and groyne constructions can be thought of, ranging from permeable wooden pile groynes as used in the Brahmaputra river in Bangladesh (Klaassen et al., 2002) to impermeable concrete groynes (Rammbuhnen) as applied in the Oder river in Germany (Nakel, 1970). In order to find out the advantages and disadvantages of various groyne designs four different types of groynes have been investigated by Uijttewaal et al. (2002). The main motivation for that study was the idea that the flow around the groyne tip can be manipulated such that the mixing layer downstream has a low turbulence level. It is expected that a quiet mixing layer reduces scour and leads to a lower flow resistance of the groyne. To this end the important modifications with respect to a reference situation concern the shape of the groyne tip and the permeability of the groyne. The four different groyne types are shown in Fig. 12-7. The first groyne of type A represents a standard groyne as it is typically found in the Dutch river

238

Chapter 12

Waal. It is a straight dike perpendicular to the river bank with slopes of 1:3 on all sides.

A

M5cnr

40 cm

D

0%

20 cm 20 cm

< 2 ° 0/ \

180 cm

114 cm

(50%)

146 cm

II11 i 11III Ml''11 i IIIM ll|l 111IIII111II11111II111111111IIIIIII11111IIII MS err

8 cm 200 cm

Figure 12-7. Cross-sectional views of four groyne types, each having the same blocking area.

Variations on this design are tested in which the groyne has a slope of 1:6 in the direction perpendicular to the main flow (type B). It is expected that the large submerged tip will broaden the mixing layer between the main stream and the groyne field, thereby reducing its velocity gradient. A second variant is made permeable by replacing the solid groyne by a row of piles (type C) (Raudkivi, 1996; Klaassen et al., 2002). In this design a parallel flow will be established through the groyne field in which the

12. The Flow in Groyne Fields

239

velocity gradient could be even smaller and where vortex shedding from the tip is expected to be suppressed. The fourth design (type D) is a combination of B and C. It has the advantage that it is not protruding a large distance into the main stream as is the case for type C. For low water levels the blocking is relatively high and it is easy to construct by adapting an existing groyne. For all variants the cross-sectional area blocked by the groyne is kept constant. This implies that the area and thus the length of the permeable groyne C with a blocking percentage < 50% must be much larger than that of the impermeable groyne A. As a consequence the mean velocity in a cross-section, is the same for all variants for a given discharge. The details of the groyne configurations will determine the exact distribution of the discharge over the cross-section. Using a mean water level and groyne height of 0.25 m, and a flow velocity in the main channel of 0.35 m/s the Froude number is 0.2 and corresponds with a prototype velocity of 2m/s for standard conditions. The Reynolds number is then approximately 6-104 for the main stream and 104 for the groyne field, sufficiently large to guarantee a fully developed turbulent flow. It is further assumed that all surfaces are hydraulically smooth. In addition to the reference water level of h = 0.25 m (emerged), higher water levels of h = 0.30 m (= 0.05 m submerged) and h = 0.35 m (=0.1 m submerged) are chosen to analyse the effects of flooding. The discharge was adjusted to obtain a flow velocity of 0.35 m/s in the main channel for all cases resulting in 0.24 m3/s, 0.31 m3/s, 0.38 mVs for the respective water levels, irrespective of the groyne type. Measures were taken in order to provide an optimised inflow of water, i.e. the inflow conditions were adapted to the expected profile far downstream such that beyond the first two groyne fields the flow could be considered as fully developed. Velocities were measured at various locations with emphasis on the shear layer and the area around the groyne, using particle tracking velocimetry (PTV). With this technique the characteristic spatial resolution is about 5 cm which is not sufficient to resolve the full spectrum of turbulent fluctuations. The conclusions that are drawn from these experiments do therefore only apply to the large scale turbulence structures. These structures are expected to contribute most to the total turbulence intensity and the associated transport processes. From the data that has been gathered a subset of the PTV-experiments will be presented, indicated by the shaded area in Fig. 12-8. This area is of particular interest since it illustrates the major effects caused by the design of the groyne head. The mean circulation in the groyne field follows a pattern similar to what was found in previous experiments or in comparable geometries (Rehbock, 1926; Chen and Ikeda, 1997; Uijttewaal et al., 2001; Weitbrecht and Jirka, 2001). The submerged part of the tip is indicated by the dotted line and the

240

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crest of the groyne by a solid line. The dash-dotted line points out the edge of the shallowest part of the groyne field. At the groyne tip the flow is forced to move either into the upstream groyne field or over the submerged 1:3 slope of the tip (indicated by the dotted line). Near the tip the velocity gradient is highest decreasing gradually downstream with the widening of the mixing layer.

4.5 m 4

P

rd

3 groyne field

4 th groyne field

field

Main stream (0.35 m/s)

30 m

Figure 12-8. Top view of the experimental set-up in which the groyne of the previous figure were built, and for which the data obtain in the gray area will be given below.

2.25

-0.5

-0.25

0

0.25 x(m)

0.5

0.75

-0.5

-0.25

0

0.25 x(m)

0.5

0.75

Figure 12-9. Velocity magnitudes (m/s) around the tip of impermeable groyne A (left) and B (right). With a water level of 0.25 m the groynes are emerged.

A comparison between groyne A and B with respect to the mean flow velocities around the groyne head (Fig. 12-9 left and 12-9 right) shows that the gentle head slope of groyne B establishes an increased velocity in the

12. The Flow in Groyne Fields

241

area where it restricts the water depth resulting in a wider shear layer. Downstream of the groyne, the width of the shear layer remains large in comparison with the groyne of type A. The accumulation of vorticity and the formation of large structures just downstream of groyne B are hindered by the three-dimensional character of the flow over the groyne tip. The permeability of groyne type C results in a unidirectional flow in the groyne field (Fig. 12-10 left). In contrast with the impermeable groynes, the momentum transfer by the water flowing through the groynes prevents the formation of a recirculating flow. With the permeability distribution used here the flow through the groyne field is slow and rather uniform. The transition of this low-speed area to the fast main stream is still found in a rather narrow band just downstream of the groyne tip. The associated high velocity gradient gives rise to the formation of a mixing layer in which large turbulence structures are developing. When compared with type C, the pattern of the mean velocity observed with groyne type D as shown in Fig. 12-10 (right) shows a rather smooth flow with only a small disturbance due to the groyne. Although the time averaged flow appears very smooth, the velocity around the groyne exhibits strong time-dependent fluctuations. It appears that the momentum entering the groyne field through the permeable part of the upstream groyne is in competition with the momentum entering the groyne via the mixing layer and the stagnation point at the downstream groyne. The return flow due to the latter cause hits the incoming flow which results in oscillating flow field.

-0.5

-0.25

0

0.25 x(m)

0.5

0.75

1

Figure 12-10. Velocity magnitudes (m/s) around the tip of permeable groyne C (left) and D (right).

A similar effect is observed with impermeable groynes under submerged conditions. The recirculating flow pattern of the emerged case interacts with the unidirectional flow in the top layer again causing strong fluctuations,

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especially with groyne A. With groyne B the slope of the groyne tip suppresses the formation of a recirculating pattern and thus the oscillations. Fig. 12-11 shows the time averaged flow patterns near groynes A and B with a water level of 0.30 m. It shows that also with the submerged case the slope of the groyne tip affects the with of the shear layer. An interpretation of the flow around submerged groynes is sketched in Fig. 12-12. With very high water levels the flow over the groynes is stationary with almost parallel streamlines. The flow will detach in the vertical plane just downstream of the groyne crest. When the groynes are slightly submerged the dynamics in the flow pattern is caused by the large eddies that move through the groyne field thereby governing the amplitude variations of the flow over the groyne.

2.25 -0.5

-0.25

0

0.25 x(m)

0.5

0.75

-0.5

-0.25

0

0.25 x(m)

0.5

0.75

Figure 12-11. Flow over submerged groynes A (left) and B (right).

eddypatr Figure 12-12. Flow patterns for submerged groynes. Fully submerged; with smooth stationary flow (left), small submergence level causing a dynamic flow field governed by the interfacial vortex (right).

12. The Flow in Groyne Fields

2.3

243

The flow in real groyne fields

The impression of groyne field flows as sketched above is based on laboratory experiments on scaled and schematised physical models. It is not straightforward to transfer this knowledge to field situations. The important phenomena associated with flow separation, mixing and recirculation appear to occur also on a prototype scale. The importance of these experiments therefore lies in the analysis of the hydrodynamic processes rather than making a prediction for a specific practical case (Uijttewaal and Schijndel, 2004).

Figure 12-13. Laboratory experiment (left) (Brolsma, 1988) and field experiment (right) Sukhodolov et al, 2002) for upstream pointing groynes.

In reality many details of the flow are governed by the flow geometry and bathymetry which is in turn influenced by the flow itself. Depending on discharge and water level, the river bed will exhibit certain changing bed forms and the erosion-deposition behaviour will be influenced by the local flow conditions (Przedwojski, 1995; Yossef and Uijtewaal, 2003). It is therefore far from straightforward to give a general impression of flow patterns on a prototype scale. Handbooks on river engineering (Jansen, 1979; Przedwojski et al., 1995; Nakel, 1970) often provide qualitative pictures of the expected circulation pattern. The information is however not always consistent. Generally speaking all groyne fields show a circulation pattern with at least one gyre with the proper sense of rotation. If there is a secondary gyre it sometimes rotates in the same direction as the primary gyre, in contradistinction with the patterns shown above. The cause for the differences often lies in the bathymetry and upstream conditions or can be attributed to the limitations of the experimental set-up (scale, number of successive groynes, width). In Fig. 12-13 for example a laboratory experiment on upstream pointing groynes is compared with field observations (Sukhodolov et al., 2002). Although the general circulation pattern looks similar for both cases a comparison is hardly allowed because

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of the different flow conditions. Unfortunately field data on flow patterns in groyne fields are very scarce and rarely published in the open literature (Sukhodolov et al., 2002; Muto et al., 2004). Given the complex phenomena associated with flow separation, mixing and recirculation under shallow conditions, field data are very valuable for the validation of numerical models as used for the prediction of flow, sediment transport and dispersion processes in rivers.

3.

CONCLUSIONS

In this chapter an overview was given on the various flow patterns that can be found in groyne fields. For many rivers the groynes play an important role with respect to bank stabilization. In the past decade the role of groyne fields with respect to their possible ecological function is gaining attention. In cases of accidental spills of pollutants it is important to recognise the consequences of temporary storage or possible deposition of polluted material in a groyne field. In case the nearly stagnant water of a groyne field forms the habitat of certain biological species the fate of pollutants should also be considered from this perspective (Armstrong et al., 2003). Forecasting the flow in a river with inclusion of the complex flow properties in groyne fields is therefore of great importance in view of controlling the water quality. However, the complexities of the flow require an expensive modelling approach that accounts for the large-scale fluctuating motions as well as the horizontal and vertical flow separation at a groyne. Hopefully, well tested modelling tools like Large Eddy Simulation will become available for large scale applications in the next few years (Uittenbogaard and Vossen, 2004; Hinterberger et al., 2004; Uijttewaal and Schijndel, 2004). These tools will provide insight in the important turbulence processes but will certainly not cover whole river reaches in full detail. Predicting transport processes on such large scale will still require a form of parameterisation (Weitbrecht et al., 2004). The knowledge gained from experiments with groyne-like structures can also be used to manipulate the flow near river banks in a subtle way. Properties like permeability, slope of the groyne tip, and inclination of the groyne can be exploited for that purpose.

ACKNOWLEDGEMENTS M. van der Wai of the Road and Hydraulic Engineering Division of the Ministry of Transport, Public Works and Water Management is gratefully

12. The Flow in Groyne Fields

245

acknowledged for supporting this research. The author is indebted to Ida Wallast, David Lehmann, Michelle Berg and Mohamed Yossef for their contributions to the experimental work.

REFERENCES Altai, W., and Chu, V. H., 1997, Retention time in a recirculating flow, In F. M., Holly Jr., and A., Alsaffar, eds., Proceedings oflAHR 27th Congress , San Francisco, USA. Arlinghaus, R., Engelhardt, C , Sukhodolov, A., and Wolter, C , 2002 Fish recruitment in a canal with intensive navigation: implications for ecosystem management, J. Fish BioL9 61:1386-1402. Armstrong, J. D., Kemp, P. S., Kennedy, G. J. A., Ladle, M., and Milner, N. J., 2003, Habitat requirements of Atlantic salmon and brown trout in rivers and streams, Fish. Res., 62, 143-170. Babarutsi, S., Ganoulis, J., and Chu, V. H., 1989, Experimental investigation of shallow recirculating flows,/. Hydraul. Eng., 115(7):906-924. Brinke, W. B. M., ten, Kruit, N. M., Kroon, A., and Berg, J. H., van den, 1999, Erosion of sediments between groynes in the river Waal as a result of navigation traffic, Int. Assn. Sediment, Spec. Publ, 28:147-160. Brolsma, J. U., 1988, Six-Barge Push-Tow Trials, PIANC, Den Haag. Chen, F-Y, and Ikeda, S., 1997, Horizontal separation flows in shallow open channels with spur dikes, J. Hydrosci. Hydr. Eng., 15(2):15-30. Garde, R. J., Subramanya, K., and Nambudripad, K. D., 1961, Study of scour around spur dikes,/ Hydraul. Div., 87(6):23-37. Gill, M. A., 1972, Erosion of sand beds around spur dikes, J. Hydraul Div., 98(9): 1587-1602. Henning, 2000, Untersuchung zur auswirkung des Buhnenwinkels aufdie Stromungsvorgdnge in Buhnenfeldern, MSc thesis (in German), University of Karlsruhe, Karlsruhe. Hentschel, B., and Anlauf, A., 2002, Ecological optimisation of groynes in the Elbe river, In Mazijk A., van, and Weitbrecht V., eds., New insights in the physical and ecological processes in groyne fields, Delft, pp. 121-133. Hinterberger, C , Frohlich, J., and Rodi, W., 2004, Three-dimensional and depth-averaged Large Eddy Simulation of shallow water flows, In Jirka, G. H., and Uijttewaal, W. S. J., eds., Shallow Flows, A. A. Balkema, Rotterdam, pp. 567-574. Jansen, P. P., van, Bendegom, J., van den, Berg, J. H., de Vries, M., van, and Zanen, A., 1979, Principles of river engineering - the non tidal alluvial rivers, Delftse Uitgeversmaatschappij, Delft. Kimura, I., and Hosoda, T., 1997, Fundamental properties of flows in open channels with dead zone, J. Hydraul. Eng, 123(2):98-107. Klaassen, G. J., Douben, K., and van der, Wai, M., 2002, Novel approaches in river engineering, In Bousmar, D., and Zech, Y., eds., River Flow 2002 - Proceedings of the International Conference on Fluvial Hydraulics, Louvain-la-Neuve, Belgium, pp. 27-43. Kuhnle, R. A., Alonso, C. V., Shields, F. D., 2002, Local scour associated with angled spur dikes,/ Hydraul. Eng., 128(12):1087-1093. Mazijk, A. van, 2002, Modelling the effects of groyne fields on the transport of dissolved matter within the Rhine Alarm Model, J. Hydrol, 264:213-229. Muto, Y., Baba, Y., and Fujita, I., 2002, Velocity measurements in rectangular embayments attached to a straight open channel, In Bousmar, D., and Zech, Y., eds., River Flow 2002 -

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Proceedings of the International Conference on Fluvial Hydraulics, Louvain-la-Neuve, Belgium, pp. 1213-1219. Nakel, E., 1970, Gewdsserausbau, V.E.B, Verlag fur Bauwesen, Berlin. Ockefeld, K., and Guhr, H., 2003, Groyne fields- sink and source functions of flow reduced zones for water content in the River Elbe (Germany), Water Sci. Technol, 48(7): 17-24. Przedwojski, B., Blazejewski, R., and Pilarczyk, K. W., 1995, River Training Techniques: Fundamentals, Design and Applications, A. A. Balkema, Rotterdam. Przedwojski, B., 1995, Bed topography and local scour in rivers with banks protected by groynes,/. Hydraul Res., 33(2):257-273. Raudkivi, A. J., 1996, Permeable pile groins, J. Waterw. Port Coast. Ocean Eng., 122(6):267-272. Rehbock, T., 1926, Das flussbaulaboratorium der Technischen Hochschule in Karlsruhe, VDI-verlag, Berlin. Richardson, E. V., Stevens, M. A., and Simons, D. B., 1975, The design of spurs for river training, In Proceedings oflAHR 16th Congress, Sao Paulo, Brazil, pp. 382-388. Schwartz, R., and Kozerski, H, 2003, Entry and deposits of suspended particulate matter in groyne fields of the middle Elbe and its ecological relevance, Acta Hydrochim. Hydrobiol, 31:391-399. Sukhodolov, A., Uijttewaal, W. S. J., and Engelhardt, C , 2002, On the correspondence between morphological and hydrodynamical patterns of groyne fields, Earth Surf. Process. Landforms, 27:289-305. Uijttewaal, W. S. J., Lehmann, D. and Mazijk, A., van, 2001, Exchange processes between a river and its groyne fields: model experiments, J. Hydraul. Eng., 127(11):928-936. Uijttewaal, W. S. J., Berg, M. H., and Wai, M., van der, 2002, Experiments on physical scale models for submerged and non-submerged groynes of various types, In Bousmar, D., and Zech, Y., eds., River Flow 2002 - Proceedings of the International Conference on Fluvial Hydraulics, Louvain-la-Neuve, Belgium, pp. 377-383. Uijttewaal, W. S. J., and Schijndel, S. A. H., van, 2004, The complex flow in groyne fields: numerical modelling compared with experiments, In M., Greco., A., Carravetta, and R., Delia Morte, eds., River Flow 2004 - Proceedings of the Second International Conference on Fluvial Hydraulics, Napoli, Italy, pp. 1331-1338. Uittenbogaard, R. E., and Vossen, B., van, 2004, Subgrid-scale model for quasi-2D turbulence in shallow water, In M., Greco., A., Carravetta, and R., Delia Morte, eds., River Flow 2004 - Proceedings of the Second International Conference on Fluvial Hydraulics, Napoli, Italy, pp. 575-582. United Nations, 1953, Economic commission for Asia and the far east, River training and bank protection, Flood control series 4, Bangkok. Weitbrecht, V., and Jirka, G. H. J., 2001, Flow Patterns and Exchange Processes in dead zones of Rivers, In Li, G., ed., Proceedings of IAHR 29th Congress, Beijing, China, theme B, pp. 439-445. Weitbrecht, V., Uijttewaal, W., and Jirka, G., 2004, 2D Particle tracking to determine transport characteristics in rivers with dead zones, In Jirka, G. H., and Uijttewaal, W. S. J., eds., Shallow Flows, A. A. Balkema, Rotterdam. Yossef M. F. M., and Uijttewaal, W. S. J., 2003, On the dynamics of the flow near groynes in the context of morphological modelling, In Ganoulis, J., Prinos, P., eds., Proceedings of IAHR 30th Congress, Thessaloniki, Greece, CII:361-368.

Index admixture 122 advection 5, 15, 18-21, 28, 31, 35-36, 51, 69, 86, 116, 126, 189, 190, 219, 227 differential 35, 72 longitudinal 164, 165 advection-diffusion equation 18, 28, 126 advection-dispersion equation 19, 21, 69, 85,90-99, 105, 116 advective pumping model 221, 223-225 aggregated dead zone model 86, 90-91, 97-99,105-107,116,120,211 algorithm QUICK 49 SMART 48-49, 54 analytical solutions 29, 170, 182 autocorrelation function 124-125, 138, 139 bedforms 210, 216, 223-224, 228-229, 243 Bessel function 179-180, 184 Boussinesq closure 217-219 channel compound xi, 36,44, 55-56, 59, 64, 67-68, 70-71, 75, 82-83, 121-122, 129-130, 140-141 main channel 25-26, 31-33, 50-52, 5556, 64-65, 70-75, 78-80, 83, 86-87, 92-93, 100-105, 121, 129-144, 150,156-162,166,169,191,219, 221,231-241 meandering xi, 32-33, 88, 90, 101, 104-106 trapezoidal 80-83, 89-93,105 two-stage xi, 121, 130, 140-141 uniform 19-22, 75, 85, 141-145 coefficient diffusion 37, 122, 126-127, 138-140, 218-219,222-223

dispersion xi, 21, 28, 31, 69-84, 90-93, 99, 159, 163, 167, 173, 192 longitudinal mixing 92-94 mass transfer 143-144, 156-162, 166167, 220 optimised mass-transfer 156-166 partition 224 proportionality 159, 162-164, 167, 191 skewness 133, 146-158, 162-167, 178 colloids 216, 224, 226, 229, 230 concentration distribution xi, 6, 9, 16, 19, 21, 30, 48, 51, 53, 125-126, 143-144, 148-153, 161, 165-166, 171, 183, 188, 235 contaminants 215, 225, 232 heavy metal 216 inorganic 215 neutral 215 non-conservative 81 reactive 215 dam 188-189, 193 damping function 42 dead zones 6, 18, 22-28, 34, 86, 92, 99, 105, 107, 143-145, 155-169, 181, 184, 186,210,215,232,245 dead-zone model 26, 28, 144, 167, 184, 210 diffusion 5-6, 15, 18-20, 31, 35-39, 5152, 122-128, 138-143, 218-223, 227 coefficient 37, 122, 126-127, 138-140, 218-223 equation 143 molecular 35, 38, 47, 125, 217-218 relative 128, 139-140 tensor of turbulent diffusion 36, 3839, 47, 126-127 turbulent 18-20, 35-39, 47, 51, 72, 123-127, 131, 137-141

248 diffusive model 216, 218, 222 dike 231, 238 Dirac pulse 192 discharge of pollutants x, 2-3, 17, 81, 109 accidental release 2, 17, 32, 192 instantaneous release 2, 18, 144,170 dispersion xi, 2, 17-22, 25, 28, 31-36, 56, 66, 69-86, 90-101, 106-107, 119, 126, 133, 140-141, 159, 163, 167-168, 173, 183-184,188,192,198,208,219, 224, 227-232, 235, 244 coefficient xi, 21, 28, 31, 69-84, 9093, 99, 159, 163, 167, 173, 192 longitudinal xi, 19-20, 32, 69, 71, 8486, 94, 98, 101, 105-107, 119, 144145, 156, 162-169, 183-184, 190, 210,218-219 numerical 29 transverse 122, 159, 162, 164, 166 distortion 187, 195 dye 18, 21-23, 26, 35, 55, 89, 110, 122, 141, 233-234 eddy 5-6, 20, 32, 36, 38-39, 42, 51, 5568, 73-74, 85-86, 125-127, 139, 140, 158, 234, 242 horizontal 55-59, 64-65 eddy viscosity 36-39, 51, 58-61, 64-67, 73-74 Elder formulation 61-65 emission limit values 3-4, 9-12 energy line 189 environmental quality standards 3, 4, 916,33 experiments 21, 34, 64, 70, 109-112, 117, 119,122,129,143,148-149,152, 155-158, 162, 164, 167, 183, 186-187, 210, 228-229, 232, 239, 243-246 exponential distribution 150, 216 far-field 5, 8, 16, 34 Fickian diffusive term 222 filtration 204, 215, 226 finite differences 74, 190 floating particles 122, 130, 133, 137 floodplains 56, 70, 75, 78-80, 83, 121, 129, 131-134, 138-141 flow resistance 237 flux of buoyancy 5

Index of mass 3, 15,40,217,218 of momentum 5,218 four-third law 127 friction 5, 47, 55, 59-61, 64, 67, 73, 188, 236 friction velocity 5, 47, 59, 61 Froude number 189, 239 Gaussian distribution 20, 170-177 generic mixing length 41-43 global coordinate system 41-44 groin xii, 18, 22-34, 56, 141, 143, 158167,231-246 groin field xii, 22-34, 56, 141, 143, 158167, 231-246 groundwater 186, 188, 212, 215, 230 gyre 233-235, 243 hyporheic exchange modelling 216 hyporheic zone xi, 185-192, 195, 200, 204, 209-212, 215, 219, 222, 229-230 image processing system 130 in-bank flows 83 inertial subrange 128 jet 4, 9, 57, 59 kurtosis 127, 134, 171 Lagrangian xi, 29, 122-128, 138-141 macroscale 125, 140 method 123 particle tracking model 29 turbulent diffusion 126-127 Lake of Biel 149, 153, 162, 164 laminar flow 35, 61 Laplace transform 144, 170, 173-179 large eddy simulation 61, 62, 66, 68, 244245 lateral canal 143, 150, 154, 162, 165 lateral inflow 87, 143 linear regression 150 local coordinate system 41, 43-44 logarithmic profile 58 longitudinal mixing coefficient 92-94 low-land river 55 Manning

249 formula 188 roughness coefficient 189, 192 mass transfer coefficient 143-144, 156162,166-167,220 mass transport equation 217 mathematical models x, xi, 14, 69, 109, 116,227 MATLAB 156, 162, 167 meandering xi, 15, 32-33, 84, 88-101, 104-106, 111,186,231 mixing cross-sectional 72, 89 horizontal 7, 234 lateral 8, 9, 12, 188 mixing process xi, 4, 7-16, 21, 32, 3536,55,68,90-101,109,121,127, 140, 161, 198 molecular 5 transverse 19-21, 31-32, 72-74, 79, 144, 159-167 vertical 7-9, 72 mixing distance 21-22, 188 mixing layers 56-60, 67-68 mixing length hypothesis 36-38, 53 mixing zone xi, 2, 4, 12-17, 32, 35, 120 Navier Stokes equations 48, 61 near-field 5, 9 nitrate 185, 211, 230 normal turbulent stresses 36, 40 numerical modelling xi, 50-51, 54, 56, 60, 64-66, 74-75, 83, 186, 244, 246 one-dimensional model 186, 235 one-way coupling 123 optimised mass-transfer coefficient 156166 over-bank flows 22, 80-84 oxygen exchange 185 partition coefficient 224 passive pollutants xi, 35-36, 47, 50-51 passive solutes 216, 218, 223-225, 229 Peclet number 31 permeability 223, 227, 232, 237, 241, 244 phosphorus 11, 186,229 physical models 56, 243 pollution ix, x, xi, 1, 2, 4, 24, 69, 81-82, 109,112,153,209,232 pollution cloud 125-126, 153

porous boundary 215, 221 porous media 224 proportionality coefficient 159, 162-164, 167, 191 pumping 191, 212, 220, 223, 226, 230 redox potential 185 regulated river 18, 187-189, 194-197, 202-205, 208-209 reservoir 193-194, 197, 206-208, 216 residence time 15, 30, 86, 169, 185, 188, 190-192, 197-198, 203-209, 216, 223226 residence time function 216, 223-226 retention 18, 30-31, 102-103, 185-188, 195, 208, 211-212, 225-227, 230-234 Reynolds analogy 36, 39, 54 equations 37, 61 number 26, 42, 68, 222, 239 stress 36, 61 Richardson 127-128, 139-140, 216-218, 229, 232, 246 law 128, 139-140 river Aare 149, 150, 153, 162-167 Brahmaputra 237 Elbe 24, 231, 245-246 Lule 186-208 Mosel 149, 153-154, 164-168 Neckar 154, 158, 161 Rhine 8, 10, 17, 22-24, 143-168, 183, 231,245 Waal 158, 238, 245 rotation 243 roughness 5, 7, 47, 73, 106, 192 Schmidt number 39, 52 sediment 32, 190, 196-197, 202, 206, 212,215-231,244-245 separation process 131 shallow flows 57, 59, 61 shallow rivers 144, 158 shear flow 19, 20, 22, 33, 55-59, 63, 127, 138, 141,228 shear layer 26, 65, 68, 121, 141, 158, 239-242 shear stress 5, 36, 38, 41,46, 54, 58-60, 73, 74, 106 side pocket 215

250 skewness xi, 22, 23, 30, 107, 127, 133, 143, 146-158, 161-168, 171, 183-184, 197 skewness coefficient 133, 146-158, 162167, 178 solute cloud 125-126, 153 sorbing solutes 216, 225, 230 sorption 32, 211, 215-216, 224-225, 228, 230 statistical characteristics 133 stochastic processes 87 storage zones 105, 220 stream-subsurface exchange 216, 220, 229 temporal concentration 85-86, 88, 96, 102, 105, 126 tensor of second moments 124-128, 138, 216, 220-226 tensor of turbulent diffusion 36, 38-39, 47, 126-127 tracer 14, 21-24, 54, 70, 85-86, 89-90, 97, 98, 101, 109-122, 143, 148-170, 186187, 191,211,224-230 transient storage model v, 85, 88, 105106, 124, 126, 138, 216, 220-230 tributary 149, 161, 166, 188 turbulence xi, 5-9, 15, 18-20, 25-26, 3351, 54, 57, 58-68, 72-73, 84, 107, 121133, 137-141, 158, 217-222, 226-232, 237,239,241,244 homogeneous 123-126, 141 models 61, 141

Index structure 51, 121, 123, 127, 140, 158, 239, 241 turbulent diffusion 18-20, 35-39, 47, 51, 72, 123-127, 131, 137-141 intensities 127 kinetic energy 60 normal stresses 36, 40, 44 two-point statistics 122 unit peak attenuation curve 117-118 variance 21, 29, 87, 90, 97, 102-103, 125127, 134, 140, 152, 171, 177, 197 vegetation 144 video camera 122, 130 viscosity 36-37, 47-50, 61, 64 viscous stress 61 visual method 122 vortex 59, 63, 233, 239, 242 vorticity 26-27, 59, 66-67, 241 wake 17, 32, 42, 57, 59-60, 63, 67 wall functions technique 46 Water Framework Directive xi, 2-4, 9, 10-14, 17, 33-34 water pollution 1, 3, 11-12, 33 water quality ix, x, xi, 1-3, 9, 12-19, 3233, 112, 153, 166, 195, 210, 227, 232, 244 wave number 57, 62