The field measurement of sediment transport parameters in estuaries

Estuarine, Coastal and Shelf Science (1990) 30, 167-183

The Field Measurement of Sediment Transport Parameters in Estuaries

J. R. West, K. 0. K. Oduyemi”, A. J. Baleb and A. W. Morrisb Department of Civil Engineering, University of Birmingham, Birmingham Bl5

2TT, “Department of Civil Engineering, Dundee Institute of Technology, Dundee DDl 1HG and bPlymouth Marine Laboratory, Plymouth PL13DH, U.K.

Received 203une 1987 and in revisedform 183uly 1989

Keywords: estuaries; fall velocity; flow measurement; particle size; shear stress; suspended solids concentration; turbulence

Field measurements have been made in the upper reaches of a partially mixed estuary in order to evolve a system of measurements that would provide insight into the parameters associated with the transport of the cohesive and granular sediment mixtures found in the turbidity maximum reaches of estuaries. Measurements were made with electromagnetic current meters, siltmeters, an Owen tube and an in situ particle size analyser. The data were analysed in order to determine relationships between particulate concentrations, fall velocity, suspension density, turbulent mean velocity and bed shear stress. The usefulness of these initial results and of the experimental techniques are discussed and some ideas for further work are presented.

Introduction

Sediment transport in open channel flow is generally governed by turbulent transport due to bed generated turbulence. Semi-empirical expressions, relating the variation of discrete particle concentration over the depth of flow to hydrodynamic conditions, have been available for steady uniform flow for many years. There is little agreement on expressions for cohesive sediment transport.

In estuarine channels, bed sediment characteristics, such as size and organic matter content, can show a considerable spatial variation in the longitudinal, transverse and vertical coordinate directions. Thus, suspensions in the time-dependent tidal flows may be expected to exhibit a wide range of particle size, density and organic to mineral matter ratios, particularly as both flocculated and discrete particles will often be present.

Many workers have tackled the complex task of developing an understanding of the hydrodynamics of estuarine suspended sediment transport processes, but many problems still remain. This paper briefly reviews the basis of discrete particle sediment transport in steady flows and then describes several techniques which are thought to be useful for the study of estuarine sediment transport processes. Some examples of results are given and some future work suggested. These should result in a more rational approach to the prediction of sediment transport in estuaries.

0272-7714/90/020167+ 17 $03.00/O @ 1990 Academic Press Limited

168 7. R. West et al.

Previous work

In steady uniform open channel flow over a bed of granular sediment, the bed generated turbulence leads to an upward flux < c’w’ > which is in equilibrium with a downwards gravitational flux CW~ where c is the turbulent mean particulate concentration, zu, the particle fall velocity, w the vertical component of velocity and a prime and < > indicate a turbulent fluctuation and a turbulent mean flux, respectively. In the absence of a good understanding of turbulent particulate transport phenomena the upward turbulent flux is related to the vertical turbulent mean particulate concentration gradient &i?z by a particulate turbulent eddy diffusion coefficient (E,,) to give (Vanoni, 1975)

1)

The assumption of a logarithmic velocity profile and linear shear stress distribution over the flow depth enables equation (1) to be solved to give (Rouse, 1937).

(2)

where c, is a reference concentration at a distance .z = a above the bed, h = flow depth, h- = von Karman constant and U, = shear velocity [ = J(t,/p)], ~~ = bed shear stress, p = fluid density, P=E,~/E,,,, and E,, = turbulent eddy viscosity.

For granular sediment w, may be determined from the Stokes equation for particle Reynolds numbers (w,d/o) < 0.5

w, = gd2Qp - P)

( 18pv

3)

where g = acceleration due to gravity, d = particle diameter, pP = particle density and (I = kinematic viscosity. In practice, it is necessary to make some allowance for particle shape. For the case of naturally occurring granular sediments when a range of size fractions may occur, equation (2) may be applied to each size fraction (Vanoni, 1975). The variation of the von Karman constant K in sediment laden flows is reviewed in detail by Dyer (1986). Dyer (1986) gave the reason for most workers adopting the practice of reducing x was to be able to correct for the discrepancy between their calculated shear stress values, based upon velocity profiles measured in the outer part of the flow and the actual values of the shear stress that will agree with equation (2) if p is assumed to be 1. This practice was rightfully described by Dyer (1986) to be a misinterpretation of the physics, since if the velocity profiles near to the bed are used K in sediment laden flow will be found to be almost equal to the clear water value.

If K in equation (2) is considered to be equal to 0.4 (the clear water value), it is possible to evaluate the value of j3 from velocity and concentration measurements. However, there is no general agreement on the value of p, with values both greater and less than 1 having been obtained. Values of approximately 1 and 10 have been obtained by Lees (1981) for fme sand and medium sand, respectively, whilst a value of approximately 0.2 has been obtained by Sangodoyin (1986) for fine, medium and coarse silt and by Soulsby et al. (1986) over a sandy sea bed. In order to derive the complete profile of sediment concentration in equation (2), the concentration at one level has to be predicted or measured. The precise definition of the reference concentrations C, is a particular problem in spite of numerous laboratory investigations, probably because of the difficulties of low Reynolds

Sediment transport parameters in estuaries 169

number, the distance needed for boundary layer development and secondary flow effects that are usually a feature of laboratory flume experiments.

Thus, for unidirectional steady flow over granular beds equation (2) must be used with caution as it has a limited predictive capability. The more complex solutions to a modi- fied form of equation (1) (see Hunt, 1954; Ippen, 1973) do not avoid the above basic limitations. For fine particles which exhibit cohesive properties, the erosion rate from the bed is a complex function of particulate properties and time, thus the reference concentration is extremely uncertain. The particle fall velocity will be a function of floe size and density which will vary strongly with time and space, depending on the velocity shear and particulate characteristics.

In the upper reaches of estuaries a mixture of granular and flocculated materials may be anticipated with the coarser material in the main channels and the finer material on the banks. Little attention has been given to evolving transport equations for these suspensions. For dilute suspensions (< 3 kg m-3) the fall velocity may be given (Odd & Owen, 1972) by

wf = kc” (4)

where k and m = coefficients which are site specific but generally of the order of 10P5--10m7 and 1-2, respectively, if wr and c have the units of m s-l and kg mP3. Measurements of turbulent mean profiles of particulate concentration have shown (Sangodoyin, 1986) that even when tidally induced acceleration and fluvially induced longitudinal density gradients are present then about 90°j0 of the concentration profiles may be approximated by an equation of the form of equation (2).

Recent developments in the measurement of shear stress (West et al., 1986) and in in situ

particle size analysis (Bale & Morris, 1987) could permit a better understanding of the applicability of equation (2) to estuarine particulate transport processes. The likelihood of such progress is examined in this paper.

Data collection

In order to form a basis for discussion, data were collected near to the centre of the channel in the upper reaches of the Tamar estuary, South West England (Figure 1, location map) at a point about 500 m south of Cotehele Quay. At high water, the channel is about 100 m wide and fairly straight for about 250 m upstream and downstream of the measurement point.

The vertical distribution of the horizontal mean velocity of water was measured over 100 s intervals using an array of Braystoke current meters mounted at 0.25 m intervals on a 2 m mast, with the current meter closest to the bed, placed at z = 0.25 m above the bed. Pump inlets were positioned at four points on the mast. They were carefully positioned parallel to the direction of flow, and away from positions which might interfere with the rotation of the Braystoke propellers. Samples for suspended solids concentration determination were collected from the pumps in 250 ml bottles and stored for filtering within 48 h. Salinity readings were obtained by using EIL MC5 salinometers, the calibration of which was checked before and after the survey. The vertical profiles of suspended solids concentration were also measured by Partech siltmeters.

Shear stress was calculated from electromagnetic current meter (mounted on a bed frame) measurements at 0.5 m above the bed. The analogue signals of the electromagnetic velocity measurements were monitored by a telemetry system, which permits the

170 J. R. West et al.

Figure 1. The Tamar Estuary

measurement of up to 12 channels of turbulence signals and their transmission to a shore- based micro-computer. The analogue signals underwent an analogue to digital (A-D) conversion, four channels were then multiplexed and the data transmitted on one of three frequencies in the 458.5-458.8 MHz band (Brierley et al., 1986). On shore, the signals were recorded on a Racal Store 4FM tape recorder, for subsequent analysis. The tape recorder was operated by 240V AC supply, whilst the velocity transducers and transmitters and receivers of the telemetry system were operated by 12 V batteries.

Surface water level gradient was measured by staff and level over a 3 km section (Cotehele Quay to Halton Quay, see Figure 1). The size distribution of suspended solids was measured with an in situ laser diffraction particle size analyser, recently developed by the Plymouth Marine Laboratory, Plymouth, U.K. (Bale & Morris, 1987). Particle fall velocity measurements were made with an Owen tube (Owen, 1976). Both the turbulent fluctuations and mean measurements were taken on a vessel situated at the centre of the channel, though on different sides of the vessel. The particle fall velocity measurements were made on the same vessel.

In statistical data processing, the record length is very important, as it can affect the accuracy of the statistical parameters of turbulence. The wide range of turbulence and


secondary flow scales that exist in estuaries makes the definition of a precise interval for determining turbulent fluxes impracticable. Soulsby (1980) has examined the criteria necessary for selecting record length and digitization rate for near-bed turbulence measurements in well mixed open sea tidal streams and concludes that a record length of the order of 600 s is required to minimize errors in turbulence parameters and Reynolds stresses. The lengths of record used in this study were 410 s and 820 s. In order to minimize the effect of tidal variation and of the probably channel topography induced shorter period wavelike fluctuations (typically with a period of N 200 s) on the values of the turbulence parameters, the records were divided into 102.4 s lengths. Linear trends were removed from them and ensemble means of eight subrecords were used to calculate the turbulence parameters. Stationarity tests (Bendat & Piersol, 1971) applied after linear trend removal showed that stationarity at the 95Oh confidence limit was obtained for all the runs.

Data analysis and discussion

Data were collected during an ebb tide and a flood tide with the intervening low slack water occurring at 14.45 hours B.S.T. The depth mean values for the velocity, salinity and suspended solids concentration are shown in the top most plot in Figure 2(a). Collection of mean measurements of velocity, salinity and suspended solids concentration was limited during the period 13.00 hours to 16.00 hours because most of the transducers were out of water during the greater part of this period. The remaining plots in Figure 2(b)-(d) show the vertical profiles of the turbulent mean velocity, salinity and suspended solids concentration. Here, the distance above the bed is plotted as a vertical line on the plots, each line showing the time at which the vertical profile was measured. The deviation of the vertical profile from the vertical line represents the turbulent mean values relative to the depth mean value, the scale being given above each plot. It should be noted that the vertical line that corresponds to a vertical profile on each plot has the same count number from each end as the profile (i.e. the third profile from the left corresponds to the third vertical line from the left).

The salinity vertical gradients are larger during the ebb tide and the maximum particulate vertical gradients occur near to the bed during the flood tide. On the ebb tide, the velocity profiles show large velocity shear in the region of large particulate or salinity vertical gradient. On the flood tide, the velocity profile peaks at approximately 1 or 2 m below the water surface level and then decreases slowly towards the water surface. The depth mean particulate concentration is generally nearly in phase with the depth mean velocity except just after the period of the large solute induced vertical density gradients which tend to suppress vertical turbulent transport processes and hence particulate transport on the ebb tide (10.00-l 1 .OO hours).

Equation (2) suggests that if the appropriate conditions are satisfied then a plot of log(h/z - 1) against log c should yield a value of the exponent Z= w,/~Ku+. Examples of ebb tide and flood tide data are given (Figure 3). These plots contain both siltmeter and gravimetric data, but when regression lines are fitted to the data the average of the two data sets is used where data have been double plotted. A plot of gravimetric against siltmeter determination of particulate concentration showed an approximately 1: 1 relationship up to 1.2 kgme3 (Figure 4).

The logarithmic plots of particulate concentration show that fairly good logarithmic approximations occur for ebb tide data but not for the flood tide data. The flood tide


Scale for deviation of mean velocity profiles frorp their depth mean values given above,

B 9 IO II 12 I3 I4 15 I6 17 I8 I9

5

( c ) Salinity 5 (9 1-v 4- -

3-

0 8 9 IO II 12 13 I4 I5 I6 I7 I8 19

Time (hours BST)

Figure 2. Velocity, salinity and suspended solids concentration data at Cotehele (817;86). In graph (a): +, velocity; 0, salinity; and 0, suspended solids concentration. The vertical lines in graph (b), (c)and (d) represent the time at which the depth mean values of velocity, salinity and solids were evaluated

Sedimenr transport parameters in estuaries 173


0 0.5 I.0 I.5 2-o

c,,,, (kg mm’)

Figure 4. Comparison of siltmeter and gravimetric particulate concentration values

results probably reflect the strongly non-logarithmic nature of the velocity profiles which have maximum values remote from the free surface. This indicates a nonlinear shear stress distribution resulting from the effects of the acceleration and longitudinal density terms in the longitudinal momentum equation. During the ebb tide period 11 .OO-12.30 hours the au/& term is comparatively small and the longitudinal solute induced density gradient is zero as the salinity is approximately zero (see Figure 2). Further discussion of the 2 values obtained from the ebb data (Figure 3) requires data for bed shear stress (5, = pu*‘), and particle fall velocity.

Shear stress was calculated from turbulence measurements of velocity at 0.5 m above the bed for a period between 10.53-12.00 hours. The bed shear stress was calculated assuming a linear variation of shear stress between the bed and the surface (t = 0). This assumption is not entirely satisfactory as the velocity profiles (Figure 2) are not a close approximation to a logarithmic variation, but are at least less irregular than the flood tide values. Furthermore, the longitudinal surface slope and shear stress terms are dominant in the momentum equation at this stage of the ebb tide. Also, the relative depth values for z = 0.5 m are fairly small (0.20-0.33) and thus the calculated shear stress values should be of the same order as the bed shear stress values in this bed generated turbulence regime.

Previous work (Oduyemi, 1986) has shown that bed shear stress has a fairly close relationship with the mean velocity at z = 0.25 m (u,-&. Data are shown in Figure 5 for bed shear stress (7,) evaluated from turbulence measurements plotted against the square of the mean velocity at 0.25 m from Braystoke measurements. A least-square regression line constrained to go through the origin of the present data gives

701 = 3.7 u;.2g (5)

which is close to to= 3.4 ui.,, obtained for r, > 0.4 N mP2 by Oduyemi (1986) in the same estuary.

A partial check on the 7, values may be obtained by calculating r,

dn 702 = pgh-

ax (6)


Figure 5. Bed shear stress variation with u,,,

0 ror(=pgh 87)/0x) (N m-*)

Figure 6. Comparison of bed shear stress values ( n , flood tide data; 0, ebb tide data)

where &l/ax = longitudinal surface slope which was also measured for the observation reach (Halton Quay-Cotehele see Figure 1). For periods when uo.25 was measured, values of rol from equation (5) and r02 from equation (6) were compared (Figure 6). The comparison is reasonably good considering that ~~~ is a 3 km reach averaged value and that zO1 is a point value which includes the scatter implicit in the approximation of equation (5). There is reason to have some confidence in the shear stress measurements and relationships of the form of equation (5). The scatter shown in Figure 6 is probably partly due to large particulate induced density gradients suppressing turbulent transport processes and hence affecting both of the parameters t, and u(z).

It is useful to anticipate a relationship between bed shear stress and particulate concentration since sediment transport is most active during periods of high bed shear stress in a tidal cycle. Figure 7 shows both depth mean particulate concentration and the point value


I

(a) I.5

4 1 b)

3

Figure 7. Variation of particulate concentration with bed shear stress ( n , flood; 0, ebb)

determined at z = 0.5 m above the bed. The depth mean plot shows more scatter, again probably due to particulate induced density gradients influencing vertical turbulent transport processes, the influence increasing with distance above the bed. The near bed values (cO & appear to have a close relationship with r,,, throughout the tidal cycle. Constraining the trend line as above gives

C ,.,=2.11 To1 (7)

for the test location. As measurements of mean velocity near to the bed are more readily available than the turbulence measurements needed for evaluating soI, then this in situ investigation has shown that a pragmatic technique for specifying c, in equation (2) would be to measure c and u near to the bed (z < 0.5 m). Then only a few turbulence measurements, which are more difficult to make, would be necessary in order to determine the relationship between r, and u~.~~. It should be noted that r, is normally available in mathematical models to drive the sediment transport processes.


/

17.00 time

(B.S.T.)

12.17

15.13 13.48 II.00

Settling tube parttculate cancentratlan (kg ti3)

0

Figure 8. Variation of mean particle fall velocity with settling tube particulate concentration

The fall velocity determination is time consuming, so only five data points are available (Figure 8). As anticipated from previous work, equation (4) is appropriate to relate the average fall velocity (wf) to the initial concentration in a settling tube. Very similar results to those in Figure 8 have been obtained by Owen (1970) and Odd (1982) for estuary mud, though their results were obtained in the laboratory. Dyer (1986) argued that the increased frequency of interparticle collision as concentration is increased causes enhanced flocculation. This results in larger, low density floes, the net effect of which is to cause an increase in settling velocity. However, it is possible that this argument may not hold for settling in a naturally turbulent shearing flow or for a settling velocity experiment done in as near a natural state as possible (i.e. in an Owen tube in the field) because of the difference in flocculation states. The direct measurements of settling velocity for this study were taken immediately in the field, before drastic change in the floe structure could occur. The physical basis for zur increasing with c is discussed later.

The in situ particle size measurements were made by measuring vertical profiles. The data on an individual profile showed considerable scatter in their median (d,,) values, thus depth average values are plotted against time in Figure 9(a). The 1Omm gap through which the suspension passes gave acceptable results (obscuration < 0.5, log error between 3-5) for c,< 500 mg-‘, where obscuration is used in relation to the muddiness of suspension and the log error is a size fitting parameter. At higher concentrations, the large number of particles can cause interference which results in the recorded d50 values being smaller than the actual values. This effect is accentuated by smaller particles. Laboratory


(a) Obscuration <0.5 Obscuration ~0.5 Obscuration ~0.5

400 _ I I

Time ib)

400 I

F 2 300-

:: -a

P ; 200 -

& 0 c ‘a $ loo em

B

0 n

I , I 0 0.2 0.4 0.6 0.8 I.0 I

r,, (N m?

Figure 9. Variation of depth averaged d,, with (a) time and (b) bed shear stress ( W, flood; l , ebb)

tests on discrete (&, - 8 urn) suspensions suggest that at 1000 mg 1-l the d,, value is reduced by a factor ot two. Thus, the d50 data between - 1 loo-1630 must be regarded as under estimates probably by less than a factor of two.

Figure 10 shows laboratory determined d,, values from substantially deflocculated and diluted samples collected during an earlier survey. At field concentrations of about 1000 mg 1-l the d,, value is - 25 urn. This is of the same order of magnitude as the in situ d5,, value at maximum velocity, and hence maximum shear (~uj~z) at - 1200 and 1600 hours. It seems reasonable to interpret the Figure 9(a) data as large (200-300 urn) floes dominate the low shear conditions at HSW and discrete particles (- 20-30 urn) and possibly similar sized floes dominate the suspensions found in the higher shear and faster flows found during the ebb and flood tides. This trend is confirmed by plotting Figure 9(b) the low obscuration (< 0.5) depth mean d,, data against bed shear stress (5,).

Thus, Figure 9(b) suggests that d50 decreases with increasing settling tube particulate concentration. This is presumably due to the combined effects of the shearing of large floes and the erosion of particles from the bed as shear stress increases, the eroded particles being larger than the constituent particles of the floe but smaller than the typical slack


0 0.4 0.8 I.2 I.6 2.0

c (kg mm3)

Figure 10. Variation of particle size (d,,) with particulate concentration.

TABLE 1. Calculation of particle density @,)

Time (hours BST)

d (de;th

averaged)

(w)

zuJ from Stoke’s Law p,/p=265 assumed

zu( from settling tube

sample (mms-‘)

PJP of floe

Settling tube particulate ‘“, =

concentration 3.7 uiz,

(km-? (Nm ‘:

11.00 35 1.10 0.18 1.27 0.90 0.54 12.17 35 1.10 1.45 3.18 2.00 0.71

13.48 40 1.44 0.20 1.23 1.12 0.22 15.13 50 2.25 0.22 1.16 1.05 0.18

17.00 60 3.24 2.60 2.32 2.69 0.97

water floe sizes. Thus, it appears from equation (3) that pP must change substantially in order to explain the fall velocity variation with settling tube particulate concentration.

As a heuristic exercise the ratio pP/p has been calculated (Table 1) from the ratio of w, calculated from equation (3) assuming pP = 2650 kg mm3 and II= lop6 m2 SC’, over wi obtained from the Owen tube. A plot of pP/p against settling tube particulate concentration, c, (Figure 11) suggests that density ratio varies with settling tube particulate concentration, and hence bed shear stress (see Table 1 for the direct relationship between bed shear stress and settling tube particulate concentration). These data show that low concentrations (- 1 kg mm3), which correspond to small shear stress values in this study, consist of low density floe and high concentrations (-2.5 kgmm3), which correspond to large shear stress values and consist mainly of discrete particles having a density - 2650 kg rne3. However, the result shown in Figure 11 may be site-specific and should be treated with caution until more universal data are available to confirm the relationship.

A probable weakness in the interpretation of Figure 11 is the fall velocity determination by the Owen tube method, as suspensions are taken from a high shear regime in the channel into nearly quiescent conditions in the Owen tube. For low concentrations, where low density floes exist in the estuary, the velocity shear is small and thus the zero shear conditions in the Owen tube are a fairly close approximation to the prototype. For higher

180 J.R. West eta1

QYQ

5.0

4.0 -

0 3.0 -

-Value for Individual

/ ‘/. particle (2.65)

/ 2.0 - 0

0 ,

/ /

,,4

I.0 fl 0 -Value for clear

water (1.00)

0 1 1

I.0 2.0 3.0

Settling tube particulate concentratlan (kg m”)

Figure 11. Variation of aggregate density ratio with suspension concentration. Where c is the settling tube particle concentration (kg m ‘). (----, at least square fitted curve.)

TABLE 2. Determination of values of /?

Time (hours BST)

w,x 103 u. x 10’

bs ‘1 (ms~l) W//KU. Z B

11.00 0.18 24.9 0.018 0.128 0.14 11.30 0.25 28.3 0.022 0.155 0.14 12.00 0.92 27.4 0,084 0,302 0.28

concentrations, it is possible that the suspension could change in size due to flocculation during the one hour duration of the experiment. However, the higher concentrations have higher fall velocities - 2 mm s-’ and thus the order of 5O”,b of the suspension will settle out in about 5 min, thus allowing only a relatively short time for flocculation to take place. Therefore, the extreme values of wr for the low and high concentrations observed in this work should be of the right order.

The W, determination may be used with the Z values determined from the slopes of the concentration profiles plots in Figure 3 to calculate /?( = E,~/E,,) if K is assumed to be 0.4. The data in Table 2 show that /3- 0.2, which is consistent with previous ebb tide results obtained for silt by using similar techniques (Sangodoyin, 1986). However, the values ofb in Table 2 differ from those obtained by Lees (1981) for fine sand and medium sand. Lees (198 1) obtained B values of approximately 1 and 10, respectively. The difference between the results may be due to different sizes of sediment with the finer sediment being able to have a more general effect on the turbulence field.


Conclusions

The above results of an exploratory field survey exercise suggest that the techniques described are capable of producing useful results for the investigation of estuarine sediment transport processes and formulae. The shear stress can be determined to a good accuracy and particle size and fall velocity can be determined to a suitable level of accuracy for a useful range of field conditions. The present data help define this range and show that good results can be obtained if temporal and spatial resolutions of the data are adequate.

Particular attention should be given to:

11) Concurrent turbulent velocity measurements at several points over the whole water column to determine E,,(Z), T(Z) and t,.

12) The use of siltmeters and electromagnetic flowmeters to determine < W’C’ > directly over the whole water column so that so(z) can be investigated as a function of particulate and solute induced vertical density gradients.

‘3) The measurements of vertical profiles of turbulent mean velocity, salinity and suspended solids at frequent intervals to investigate the limits of applicability of equation (2) and to seek a more appropriate transport formula when acceleration and longitudinal density gradient effects are influential.

14) An evaluation of the Owen tube for mixtures of granular and flocculating suspensions and to making more measurements during a tidal cycle than were undertaken in the trial survey.

15) Improving the in situ size analysis by quantifying the particle size fitting obscuration corrections, changing cell path lengths and by more frequent measurements during a tidal cycle.

In general the application of the above techniques at several sites together with a careful analysis of the bed sediments should result in a considerable improvement in the knowledge of estuarine sediment transport processes and formulae.

References

Bale, A. J. &Morris, A. W. 1987 In situ measurements of particle size in estuarine waters. Estuarine, Coastal and Shelf Science 24,253-263.

Bendat, J. S. & Piersol, A. G. 1971 Random data: analysis and measurement procedures. New York: Wiley- Interscience.

Brierley, R. W., Shiono, J. & West, J. R. 1986 An integrated system for measuring estuarine turbulence. Proceedings of the International Conference on Measuring Techniques of Hydraulics Phenomena in Offshore, Coastal and Inland Waters, London, England, 9-l 1 April 1986.

Dyer, K. R. 1986 Coastal and estuarine sediment dynamics. Chichester: John Wiley and Sons, pp. 202-230. Hunt, J. N. 1954 The turbulent transport of suspended sediment in open channels. Proceedings of the Royal

Society (London) A, 224,322-335. Ippen, A. T. 1973 The interaction of velocity distribution and suspended load in streams. IAHR

International Symposium on River Mechanics, Bankok, pp. 341-369. Lees, B. J. 1981 Relationship between eddy viscosity of sea water and eddy diffusivity of suspended particles.

Geo-Marine Letters 1,249-254. Odd, N. V. M. 1982 The feasibility of using mathematical models to predict sediment transport in the Severn

estuary. In: The Severn Barrage London: Thomas Telford Ltd., pp. 195-202. Odd, N. V. M. &Owen, M. W. 1972 A two-layer model of mud transport in the Thames estuary. Proceedings

ofthe Institute of CivilEngineers Supplement IX, 175-205 (paper 7175s). Oduyemi, K. 0. K. 1986 Turbulent transport of sediment in estuaries. Ph.D. thesis, University of

Birmingham, U.K. Oduyemi, K. 0. K., Sangodoyin, A. Y. A. & West, J. R. 1990 Flow structure and sediment transport in

estuaries. (Submitted for publication).

182 J. R. Wesr et al.

Owen, M. W. 1970 A detailed study of settling velocities of an estuary mud. Report No. INT 78, Hydraulics Research Station,

Owen, M. W. 1976 Determination of the settling velocities of cohesive muds. Report No. IT 161, Hydraulics Research Station, Wallingford, U.K.

Rouse, H. 1937 Modern conceptions of the mechanics of fluid turbulence. Trans ASCE, 102, Paper No. 1965, pp. 463-543.

Sangodoyin, A. Y. A. 1986 Spatial distribution of suspended solids in the upper reaches of partially mixed estuaries. Ph.D. thesis, University of Birmingham.

Soulsby, R. L. 1980 Selecting record length and digitization rate for near-bed turbulence measurements. 3. Physical Ocean. 10, pp. 208-219.

Soulsby, R. L., Salkield, A. I’., Haine, R. A. & Wainwright, B. 1986 Observations of turbulent fluxes of suspended sand near the sea bed. In: Transport of Suspended Solids in Open Channels. Balkema, Rotterdam. pp. 183-186.

Vanoni, V. A. 1975 Sedimentation engineering, Report on Engineering Practice No. 54, ASCE, New York. West, J. R., Knight, D. W. & Shiono, K. 1986 Turbulence measurements in the Great Ouse estuary.Journul

of Hydraulic Engineering, ASCE, 112, HY3. pp. 167-180.

a

C

2

d 50

g

h k m s t u u* W

Wf

i

;

& cz & rnZ

rl

ti

u

P

PP

50

Notation

a near bed reference height turbulent mean particulate concentration or settling tube particulate concentration turbulent mean particulate concentration at z = a particle diameter mean particle diameter acceleration due to gravity flow depth coefficient coefficient salinity time horizontal component of turbulent mean velocity friction velocity vertical component of turbulent mean velocity mean particle fall velocity longitudinal coordinate direction coefficient ( = wf/@cu,) distance above bed ratio E,,/E,, turbulent eddy diffusion coefficient for particles turbulent eddy diffusion coefficient for momentum water surface elevation von Karman constant kinematic viscosity density of water aggregate density bed shear stress

Subscripts

d depth mean value inst. instrument reading


grav. gravimetric determination 0.25 measurement at z = 0.25 m 0.5 measurement at 2 = 0.5 m 01 evaluated from eqn. (5) 02 evaluated from eqn. (6)

Other notation

prime indicates a turbulent fluctuation < > indicates a turbulent mean value

Documents

The field measurement of sediment transport parameters in estuaries