The determination of estuarine diffusion coefficients using a fluorimetric dye tracing technique

Estuarine, Coastal and Shelf Science (1988) 27,297-310

The Determination of Estuarine Coefficients using a Fluorimetric Tracing Technique

I. GuymeP

Diffusion Dye

and J. R. West?’

“Department of Civil Engineering, Heriot- Watt University, Edinburgh EH14 4AS, and ‘Department of Civil Engineering, University of Birmingham, Birmingham BIS 2TT, U.K. Received 23June 1987 and in revised form 18 April 1988

Keywords: diffusion; fluorescence; tracers; estuarine circulation;

WalesCoast

An improved dye-injection techniquehasbeenusedto collect newfield datato study the transverseandvertical mixing in asectionof the Conwy estuary.These resultsdefinethe full three-dimensionalspatialconcentrationdistribution of the dye plume. Estimates of the diffusion coefficients are given and were found to be

strongly influencedby the transverseshearinduceddensity variationsand bed topography. The resultssuggestthat an analogywith Fickian diffusion appears inappropriateon flood tidesbecauseof the importanceof secondarycirculations during this tidal phase. Introduction The growing use and acceptance of mathematical models for studying the flow field and solute mixing in estuarieshas highlighted a deficiency in the present understanding of the dependence of solute transport on parameters such as: tidal range, river flow, channel geometry, bed topography and density variations. This consequently restricts the reliability of the predictions of diffusion coefficient values necessary for mixing type mathematical models and hence the reliability of the model predictions. This paper describes a seriesof field experiments performed in the Conwy estuary, North Wales, the aim of which was to estimate values of the transverse- and verticalmixing coefficients and to compare these values to ones predicted by the presently available empirical formulae. Previous work In the past, soluble tracers have been used extensively for determining mixing coefficients from prototype data. Of the tracers readily available, rhodamine, a fluorescent dye, has been found to have several advantages over other tracers such as salt solutions and radioactive isotopes. These advantages include: the low tracer concentrations detectable by modern fluorimeters, the ability to take direct readings from continuous flow samples and the relatively low cost of the equipment capable of working in most environments. 0272-7714/88/090297+

14 $03.00/O

@ 1988 Academic Press Limited

298

I. Guymer Q J. R. West

To estimate values of the diffusion coefficients from laboratory or field measurements, an assumption is made that Fickian diffusion, analogous to molecular diffusion, can be used to describe mixing in turbulent flows (Fischer et al., 1979). This allows the properties of a spreading cloud or plume to be used to determine diffusion coefficients, Q, namely Esi =

and

+

uA 2 cc -,

s-= a:

(?Oi2 -

3X

(1)

cxi2 dx, (2) c dxi

I -cm where: c is dye concentration, uA is area mean velocity, oi2 is variance of distribution in direction i, xi is Cartesian co-ordinate system, i= I,2 or 3. Laboratory studies using rhodamine tracers have been performed by Jobson and Sayre (1970) to investigate vertical momentum transfer in an artificially roughened laboratory flume, and Sayre and Chang (1968) to study the longitudinal and lateral dispersion in a rectangular channel. Mixing studies in open-channel flows with vertical density differences have been undertaken by Prych (1970) and Sumer and Fischer (1977). Fluorescent dyes have been used in several full-scale investigations, examples are: field tests conducted by Fischer (1967) in a straight sand-bed channel to determine mixing coefficients; Bailey et al. (1966) studied the dispersal of waste water and flushing characteristics in San Francisco Bay and Lee and McGuire (1973) studied outfall location and diffuser efficiency off Florida’s south-east coast. Mixing in estuaries and coastal waters has been investigated by Talbot (1974) and Bowden and Lewis (1973) who reported the results of three studies using rhodamine B tracer. There have been few attempts to measure transverse mixing in estuaries. Fisher (1972) obtained a value of the transverse-mixing coefficient, from a dye release in the Delaware estuary, equal to 1.2 du., where d is the depth of flow and U* is the shear velocity and Fischer et al. (1979) gave 0.15 du, as the best estimate of the transverse mixing coefficient from all available laboratory and field results. West and Cotton (1981) performed surface dye injections in the Conwy estuary and concluded that the transverse mixing coefficient from both laboratory data and estuary studies for open-channel flow, having a large width/depth ratio could be given as E, = 0.4(du,)“12

(3)

All workers acknowledge that the transverse-mixing coefficients obtained by experimental methods contain someeffect of transverse-flow components. Vertical-mixing coefficients have been determined from work undertaken in a laboratory flume by Jobson and Sayre (1970) who gave a depth-averaged value of the vertical-diffusion coefficient equal to 0.063 du,. West and Cotton (1981), working in a saline reach of the Conwy estuary, gave values of 0.025 du, and 0.01 du, for the verticaldiffusion coefficient measured on flood and ebb tides, respectively. Field measurements The field technique consisted of injecting rhodamine dye onto the surface of the flow and recording its position and concentration simultaneously at three levels in the flow asit was

Estuarine

diffusion

c-h

6

coeficients

Conwy

estuary

Figure 1. Location of Conwy Estuary study reach. Levels are given A-A, Position of section recording velocity and salinity variations.

in metres

(AOD:.

transported through the study reach, (Figure 1). To assist with the interpretation of these results, recordings over the vertical, of velocity and salinity, were performed from upto five fixed stations, at one transverse section within the reach, at 20-min intervals. This data will be the subject of a further paper (Guymer & West, in prep.). Rhodamine dye diluted to approximately 5 g 1-l was injected at a constant rate onto the surface of the flow from an unmanned inflatable boat. A tracking boat equipped with three fluorimeters continuously sampled the dye concentrations at fixed depths below the water surface. The position of this tracking boat as it traversed the dye plume was recorded from a single shore station using a theodolite and electronic distance measuring equipment. Full details of this field measurement technique are given in Guymer and West (1986). Data

analysis

In total, data were obtained on three flood and three ebb tides during July 1983. A summary of the available hydraulic data and the times when dye concentrations were recorded is given in Table 1. In general, four traverses were performed at each section simultaneously recording the dye concentrations at three depths in the flow. The recorded distributions were scaled to obtain actual concentration distributions. These scaling corrections were applied to both the concentration and the time scaleon the chart paper to

300

I. Guymer &J.

TABLE 1. Hydraulic

Date 1983

Tide

Tidal height0 (ml

15 18 19 14 15 18

Flood Flood Flood Ebb Ebb Ebb

8.9 7.8 7.7 9.3 8.9 7.8

July

OPredicted

R. Wesr

data and times

for dye tracing

Tidal range” Cm)

Measured area mea* velocity, uA (ms ‘1

Mean depth, yd (4

8.1 5.3 5.4 8.1 8.1 5.3

-0.55 -0.40 -0.37 0.41 0.42 0.35

2.5 2.5 2.0 2.25 2.5 2.0

Times for dye tracing 14.19-14.57 17.19-17.59 18.27-19.08 16.08-16.56 17.02-17.37 20.10-20.49

h h h h h h

values at Liverpool

allow for the individual instrument calibration, the relative concentration of the injected dye, the background concentration, the sampling rate and the boat speed. In correcting for the boat speed a uniform velocity was assumedbetween consecutive position fixes, on average a distance of around 8 m. Having obtained a set of comparable individual distributions, the distributions recorded at the samelevel at a section were then meaned in a moving-frame system (Csanaday, 1973) to produce an average distribution. Using the position fixing of the tracking boat it was possible to determine the location in plan of the centroid of each individual distribution. The position of the centroids within the test reach were then averaged for eachsection to give a mean position and allow the distance from the injection boat to be estimated. The accuracy in the longitudinal direction is dependent on the path taken by the tracking boat and the results show deviations of lessthan + 5 m in the longitudinal direction. A calculation of the dye recovery ratios (the proportion of total dye output recorded in downstream observations) wasperformed for each of the tides at both the third and fourth sectionsfrom the injection point using the detailed primary velocity measurementsmade during the experiments (Guymer & West, in prep.). Values of 0.94 + 0.13 and 0.74 f 0,21 for the flood and ebb tides, respectively, were obtained. These show a considerable improvement to the values published from previous field studies: Cotton (1978) gave values of 0+70*0.06 and 0.49 &O-O8 for flood and ebb tides, respectively, and are more consistent with the value of 1.04 f 0.17 obtained by Sayre and Chang (1968) from laboratory experiments. Discussion

A first comparison of the plots showing the change in mean transverse variance with longitudinal distance (Figures 2 and 3) illustrates the difference between the dye plumes produced on the flood and ebb tides. Ebb-tide results The results from the ebb tides (Figure 2) exhibit a more regular trend than do the floodtide results, with smaller standard errors. A closer inspection of the data used to determine the depth mean variance for ebb tides confirms that the individual and average (Figure 4) distributions measuredon eachtraverse exhibit good Gaussian-shapedprofiles, with only small changesin the magnitude of the variance over depth (Table 2). As would be expected

Estuarine

difJusion

301

coefficients

Longhdlnol

dlstonce,

x

Cm)

Figure 2. Variation of transverse variance with distance from :I, 14 July; 0, 15 July; 0, 18 July. Bars are standard errors.

500

source

on 1983 ebb

tides.

-

“E 400NZI b

I \

0

-100

-200 Longttudlnol

Figure 3. Variation 0, 15 July; 0,18

-300 dlstonce,

-400

-500

-1

x (ml

of transverse variance with distance from July; x , 19 July. Bars are standard errors.

source on 1983 flood tides.

by sampling from a stochastic process such as turbulent flow, there is a much greater correlation of the transverse variance of the dye plume with depth at a given time than with successive samples at a given depth.

302

I.

&J.

Guymer

R. West

b)

-45

-30

-15

0

Tronsverse

15

distance,

30

45

y Cm)

Figure 4. Average ebb-tide distributions for individual sample levels. (a) 225 m from the source on 15 July; (b) 399 m from the source on 18 July. Depth below surface: I, 0.5 m; II, 1.25 m; III, 2.0 m.

TABLE 2. Values during ebb tide

of transverse

Depth below water surface (4

variance

(mz) obtained

Traverse

225 m from 0.5 1.25 2.0

source,

399 m from 0.5 1.25 2.0

source,

from

dye distributions

recorded

number

1

2

3

4

Average

15 July 13.7 16.8 17.3

18.7 21.2 27.2

13.7 22.3 26.3

26.2 29.2 24.4

18.1 22.4 23.8

18 July 99.1 884 113.3

54.1 63.5 77.5

22.5 26.2 28.0

30.4 32.3 24.7

51.5 52.7 60.9

Employing the analogy with Fickian diffusion, after the initial spreading of the dye, a first-order increasein the plume variance with distance is predicted. However, inspection of the results presented for the ebb tides (Figure 2) showsa reduction in the magnitude of the transverse variance on the occasionswhen dye wasrecorded at four sections: 14and 18 July. An approximate linear increasein the transverse variance between the first and third

Estuarine diffusion coeficients

TABLE 3. Comparison coefficients

303

of measured

and

predicted

Diffusion Date July 1983 15 18 19 14 15 18

values

of transverse

coefficients,

diffusion

E,~ (cm’ s ‘) Predicted

Tide Flood Flood Flood

u.=O.O4+0~01 “From selected

Ebb

-0.34" -0.38" -0.44" 0.18

Ebb Ebb

0.12 0.10

ms-‘(Knight, data.

Measured

0.15 du.

943+500 766k400 808k400 372k140 25Ok 100

150*3s 120+30 120+30 135+34

18Ok52

150+38 120+30

0.4 (du . )’ ”

303k64 236k50 236k50 270557 303k64 236k50

1981).

sectionswas obtained on all the tides. Inspection of the individual results from the 14 and 18 July ebb tides suggeststhat the width of the plume varies very little between sections three and four, and that the inconsistency appears to be a result of an increase in the concentration of dye in the tails of the distributions (further than 15 m from the centroid) at the third section [Figure 4(b)]. A possible explanation of this effect may come from the topographical channel features. Echo soundings of the bed revealed the existence of a sand bank approximately aligned with the longitudinal axis of the channel, which raised the bed level by some 0.5 m between the second section and mid-way between the third and fourth sections. At the third section, therefore, a small transverse component of flow would be created by the water tending to flow off the sand bank and into the deeper channels at either side. While at the fourth section the increasing depth of flow would tend to promote the vertical advection of dye and inhibit the transverse spreading. These events could explain why the variance values, or2 are above and below the linear trend at sections 3 and 4, respectively. The regular distributions of dye recorded on the ebb tides justify the useof a Fickiantype diffusion model where appropriate. Linear functions, fitted using a least-squares criterion, were used to obtain estimatesof the &,*/6x term in equation (1). The oY2values at sections 1 and 2 generally being close to the fitted lines. The slopes obtained by the inclusion of either section 3 or section 4 with the first two sections have been used to determine possible errors. The results are presented in Table 3. Flood-tide

results

The flood-tide results exhibit lessGaussian-like dye cancentration distributions (Figure 5) and a greater variability of rs,,’values (Table 4) than those for the ebb tides. Thus the validity of assuming the dominance of a Fickian-type diffusion process is questionable. However, the shortage of available data from which to predict estuarine diffusion coefficients, especially for flood tides, and their requirement by all mixing-type mathematical models, necessitatesthat an analysis is attempted. The data was therefore analysed in the same manner as the ebb-tide results and the non-uniformity of the resulting plot (Figure 3) demands discussion of the individual data sets. The results for the 15July flood tide show an approximately linear increasein transverse variance with distance between sections 1 and 3, with a reduction to almost zero at section

304

I. Guymer &‘J. R. West

80-

( a)

0-

60 (

30-

0, -45

1

-30

-15

0

Transverse

15

distance,

30

45

y (m)

Figure 5. Average flood-tide distributions for individual sample levels: (a) 216 m from the source on 15 July; (b) 300 m from the source on 18 July. Depth below surface: I, 0.5 m; II, 1.25 m; III, 2.0 m.

TABLE

4. Values of transverse variance (m’) obtained from dye distributions during flood

tide Depth below water surface (4

Traverse number 1

Average

2

3

4

5

27.6 62.5 41.8

27.0 40.8 56.4

14.8 93.3 63.4

IF

22.1

30.4 36.6

53.4 83.9

49.9 97.3 105.4

54.9 173.3 197.4

75.6 148.3 150.0

55.8 172.5 193.1

49.2 144.1 153.5

2 16 m from source, 15 July 0.5

1.25 2.0 300

18.9 40.0 221.1

m from source, 18 July 0.5 1.25 2.0

10.0 128.9 121.6

IF, instrument failure. 4, approximately 500 m from the source. This was caused by the absenceof dye at the upper two sampling levels (0.5 and l-25 m below the water surface), with only a very small

quantity of dye being detected above the background concentration 2 m below the surface. Since dye waseasily detected above the background level at the third section and on other

Esruarine

diffusion

coefficients

305

tides dye has been detected up to 600 m from the source, then this result appears not to have been caused by excessive dilution. The most probable cause of this non-recovery of dye 499 m from the source is thought to be channel topography. On this tide, dye was injected some 100 m further inland than on the other two flood tides and, as a result, this fourth section was recorded closer to the Tal-y-Cafn road bridge where the channel deepens by over 2 m. It would be expected, therefore, that the faster flowing, more saline water (Guymer & West, in prep.) in the centre of the channel would, by gravitational effect, move towards the bed, thus transporting the entrained dye below the sampling levels. Average dye distributions from the second section, 216 m from the source on 15 July flood tide are presented in Figure 5(a). The individual values of transverse variance are given in Table 2 and illustrate the greater variation of transverse variance recorded on flood tides compared with ebb tides. An overall mean value of 55 + 52 m2 was obtained, with one distribution having a value of 221 m”. At the third section, dye was only recorded on two of the four traverses at the uppermost sampling level. In obtaining a mean value for the transverse variance at this section, the occasions where no dye was recorded have been omitted, because in a moving-frame system (Csanaday, 1975) these could result from vertical meandering of the plume. Data from sections l-3 inclusive give a value of the transverse diffusion coefficient of 943 cm’ s- ‘. The results for the 18 July flood tide (Figure 3) exhibit a linear trend with variations from the best-fit first-order curve of similar magnitude to those obtained from the ebb tide. The major difference between these results and those presented in Figure 2 is the magnitude of the standard errors. The standard errors obtained from the flood-tide results are generally over five times greater than those recorded during any of the ebb tides. Inspection of the individual results for the 18 July flood tide shows that this is probably due to the transfer of dye away from the surface of the flow, together with convergence at the surface and divergence at the bed caused by secondary flow effects (Guymer & West, 1986). Results from the second section recorded 300 m from the source on 18 July are shown in Figure 5(b). These results show a surface dye distribution of approximately half the concentration and one third the width of the distributions measured at the two lower sampling levels. At the fourth section, no dye was recorded at the upper sampling level, while at 2.0 m below the surface the plume had divided into two. Within the diffusion analysis no allowance has been made for this effect and, as a result, the calculated transverse variances are large. Consideration of all the available data for the 18 July flood tide produces an estimate of 766 cm’ s ’ for the transverse-diffusion coefficient, although errors of the order of + 50”,, must be anticipated because this result appears to include some effect of the secondary circulation. Results for the flood-tide experiment performed on the 19 July show similar features to the other recorded flood tides. The major difference being in the magnitude of the standard errors associated with the distributions recorded at the third and fourth sections. The individual and average distributions recorded 0.5 m below the surface at the third section 423 m from the source, are presented in Figure 6. These results show two well-defined plumes at this level on three of the four traverses. These plumes are separated by some 15 m of water containing no dye, resulting in very large values of variance being obtained. Using all the available data for the 19 July flood tide produces an estimate of 1400 cm’ s- 1, while omitting the values calculated at the third section leads to an estimate of

306

I. Guymer &J.

5 ; L ‘; t E

501

6

30-

R. West

-60 (b)

0

60

-60

0

60

40 -

20 IO Or

-60

-30 Tronsverse

Figure surface

6. Individual 423 m from

0 didonce,

30 y (ml

(a) and average (b) dye distributions the source on the 19 July flood tide.

recorded

05 m below

the

808 cm’ s-l. It appearsreasonableto omit the results from Section 3 astheseshow a strong secondary flow influence. Transverse

diflusion

Summarizing the results, for the ebb tide a Fickian analogy is probably a reasonable approximation as the transverse dye concentrations are close to Gaussian and are well ordered in both of the other co-ordinate directions. The plot giving the variation of transverse variance with distance may reasonably be approximated by a linear trend, with the effects of topography on local variations in vertical mixing and secondary flow being considered as causing minor perturbations about the assumedlinear trend. A summary of the diffusion coefficients obtained from the dye tracing experiments performed during this study on the Conwy estuary is given in Table 3. The ebb-tide experiments gave values of the transverse-diffusion coefficient, E,~,of between 180 and 372 cm* s-’ for predicted tidal range at Liverpool, between 5.3 and 8.1 m. These ebb-tide data suggestthat E,~increaseswith tidal range, which is consistent with lower bed-shear stressvalues found on neap tides (Knight, 1981).

Estuarine diffusion coefficients

307

For the flood tide, the transverse dye concentration distributions are generally close to Gaussian within 300 m of the injection point, even though vertical convection effects are clearly demonstrated. For sectionsrecorded beyond 300 m from the source, the secondary flow effects lead to departures from Gaussian characteristics which are reflected in the scatter and magnitude of the standard errors shown in Figure 3. It appears reasonableto conclude that as long as the plume dimensions are very much lessthan the scaleof the secondary flow, a Fickian analogy is permissible, but once the plume width has grown to the order of the channel half-width, then secondary flow effects become significant. Tentative values of the transverse-diffusion coefficient, .zSy,on flood tides have been obtained. These varied between 766 and 943 cm* s-l and retain some influence of the secondary flows shown to exist on flood tides in this reach. As a result, possible errors of f 50”& must be anticipated. The slight narrowing of the channel on the flood tide, and hence widening on the ebb, would have the effect of increasing the width of the plume on the ebb compared with the flood tide. This effect is not evident in the results, so the difference between flood and ebb tides is tentatively attributed to secondary flow effects induced by transverse pressure gradients as other parameters such as velocity and flow depth were not significantly different during the flood and ebb tide dye tracing periods (Table 1). Vertical

diffusion

Attempts have been made to estimate values of the vertical-diffusion coefficent from the transverse distributions of rhodamine dye recorded at the different levels in the flow. Both the plume width mean concentration value and the dye concentration at the centroid of the transverse distribution were used to obtain a representative value for the dye concentration at a particular level in the flow. However, this gave only three points over the vertical to define the dye distribution and to calculate the vertical variance of the distribution. Full details of the results are presented in Guymer (1985). Distances of around 100 m between the injection point and the first recording section resulted in the dye having reached the bed in all the 1983 experiments where the depth of flow was lessthan approximately 3 m. In addition, the complex secondary flow structure recorded on the flood tides (Guymer & West, in prep.), and reflected in the dye distributions, prevented any reliable estimation of a vertical dye distribution. As a result, no estimatesof the flood-tide vertical-diffusion coefficients have been made from this data. However, preliminary studies were performed in 1982 on a test section just seawardof the Tal-y-Cafn road bridge where the channel deepens by over 2 m. These results, although based on a less accurate method of transverse position fixing, do allow an estimate of the vertical diffusion coefficient to be made. The variation of the vertical variance, oz2,with distance is shown in Figure 7 for the ebb tides. Values of the vertical diffusion coefficient, E,, varied between 6 and 21 cm* s-’ over the majority of the flow depth. Comparison

of results

Few field measurementshave been made to obtain values for the transverse- and verticaldiffusion coefficients in open channels. Of these, only Cotton (1978) attempts to define values for the coefficients in an estuarine flow. In experiments conducted on another reach of the Conwy estuary, a single fluorimeter system was used to obtain values of the diffusion coefficients. These varied for the transverse diffusion coefficient, &,r, between 400 and 900 cm* SK*on the ebb tide and between 800 and 1000 cm*s-’ on the flood tide.

308

I. Guymer &J.

R. West

1

300 Dltance

from

Figure 7. Variation of vertical variance x, 7 July; 0,12 July; 0, 13 July.

source,

5

400

)O

Y (m)

with distance

from

source

for ebb tides in 1982:

Values for the vertical diffusion coefficient, E,,, also exhibited a significant difference between flood and ebb values, varying between 1 and 24 cm’ s--’ for the ebb tides and between 32 and 67 cm’ s-’ for the flood tides. The experiments performed by Cotton (1978) were conducted over a greater time period, with less stringent controls on position fixing than was the present study. Furthermore, measurements of flow conditions and structure were not made simultaneously. However, while the results show a greater range of values, they are of a similar order of magnitude and agree fairly well with the values obtained from the present study, when allowance is made for the limitations of each experimental technique. Equations used to predict values of diffusion coefficients usually employ two parameters: the flow depth, d, and the shear velocity, u*. The measurement of the flow depth is relatively straightforward; however, determining values for the shearvelocity in a natural environment is difficult. Knight (1981) showed the variation of a reach mean shear velocity for a reach on the Conwy estuary. These results exhibited little variation with tidal range over the periods when dye distributions were recorded and, therefore, mean values have been assumedto assessthe accuracy of the predictive equations given by Fischer et al. (1979) and West and Cotton (1981). Comparing predictions of the transverse diffusion coefficients made using these equations to actual field results (Table 3) shows the values predicted by Fischer et al. (1979) to be factors of approximately 2 and 4 too small for the ebb and flood tides, respectively. The values predicted using the West and Cotton (1981) approach appear to be of similar order of magnitude to the recorded values on the ebb tides, with the flood tide predictions being a factor of 2 too small. This difference of a factor of 2 for the flood tide t‘,, values, also found by West and Cotton (1981), is probably causedby the inability of the predictive equations to incorporate the significant density driven secondary flows shown to exist on the flood tides. Comparing predictions of the vertical diffusion coefficient, E,,, to values measured on the ebb tides, shows the depth mean values predicted by Jobson and Sayre (1970) from laboratory results to be between 4 and 15 times too large. The results are consistent with the values given by West and Cotton (1981) and are to be expected for flows containing vertical salinity gradients, shown to be present in this reach (Guymer and West, in prep.).

Estuarine

diffusion

coefficients

309

Conclusions (1) Improvements in the fluorimetric-tracing technique reported by West and Cotton (198 I), incorporating more detailed hydrodynamic data, faster flourimeter response time and better plume definition, have been shown to give better recovery ratios and, therefore? more reliable estimates of the mixing characteristics. (2) For ebb-tide results a Fickian analogy appears to give a reasonable approximation to the system as the recorded dye distributions appear close to a Gaussian form. (3) An average value of 270 cm2 s -’ for the transverse-diffusion coefficient, cSy was obtained from the ebb-tide data and the results suggest that E,~increases with tidal range. (4) For flood-tide results, dye distributions were close to a Gaussian form for distances up to approximately 300m from the source. At distances greater than 300m from the source, the secondary flow effects lead to departures from Gaussian characteristics and individual inspection of the results is required. (5) From the flood-tide results an average value of the transverse-mixing coefficient, involving effects of both diffusion processes and advection due to secondary flow, of 840 cm2 se-’ was estimated. (6) Difficulties in obtaining a good vertical spatial definition of the dye plume on flood tides made estimates of the vertical mixing parameters unrealistic, however values of the vertical diffusion coefficient, E,,, for ebb tides varying between 6 and 21 cm’ s ’ were obtained. (7) The results show that bed topography such as sand banks can affect both flood- and ebb-tide mixing processes. References Bailey, T. E., McCullough, C. A. & Gumerson, C. G. 1966 Mixing and dispersion studies in San Francisco Bay. Journal Sanitation Engineering Division, Proceedings of the American Society of Civil Engineers 92(SA5), 23-45. Bowden, K. F. & Lewis, R. E. 1973 Dispersion in flow from a continuous source at sea. Water Research 7, 1705-1722. Cotton, A. I’. 1978 On mixing coefficients in an urban stream and tidal river. Ph.D. Thesis, University of Birmingham, U.K. Csanady, G. T. 1973 Turbulent Diffusion in the Envwonment. Dordrecht: D. Reidel. Fischer, H. B. 1967 The mechanics of dispersion in natural streams. Journal of the Hydraulics Division, American Society of Civil Engineers 93,(HY6), 128216. Fischer, H. B. 1972 Mass transport mechanisms in partially mixed estuaries. Journal of Fluid Mechanics 53, 671-683. Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coaszai Waters. New York: Academic Press. Guymer, I. 1985 Some aspects of solute transport processes in the Conwy estuary. Ph.D. Thesis, IJniversity of Birmingham, U.K. Guymer, I. & West, J. R. 1986 Evaluation of estuarine mixing mechanisms using fluorimetric techniques. Imernational Itrland Waters,

Jobson,

Conference London,

H. E. 8 Sayre,

Divisions,

Proceedings

on Measuring England, 9-l

Techniques of Hydraulics Phenomena in Offshore, Coastal and I April, pp. 337-346, B.H.R.A. publication. W. W. 1970 Vertical transfer in open channel Flow. Journal of‘ the f{\tdraulic.t of the American Society of Civil Engineers 96, 703-724.

Knight, D. W. 1981 Some field measurements concerned with the behaviour of resistance coefficients in a tidal channel. Estuarine, Coastal and Shelf Science 12,30%322. Lee, T. N. & McGuire, J. B. 1973 The use of ocean outfalls for marine waste disposal in southeast Florida’< coastal waters. Sea Grant Coastal Zone Management Bulletitz No. 2. University of Miami, Fl, U.S.A. Prych, E. A. 1970 Effects of density differences on lateral mixing in open-channel flows. Report No. KH-R-21. W.M. Keck Laboratory of Hydraulics and Water Research, California Institute of Technology, Pasadena, California, U.S.A. Sayre, W. W. & Chang, F. M. 1968 A laboratory investigation of the open channel dispersion processes for dissolved, suspended and floating dispersants. U.S. Geological Survey, Professional Paper 433-E.

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Sumer, S. M. & Fischer, H. B. 1977 Transverse mixing in partially stratified flow. Journal of Hydraulics Division, American Society of Civil Engineers 103,587-600. Talbot, J. W. 1974 Interpretation of Diffusion Data. In Symposium a Discharge of Sewage from Sea Outfalls Gameson, A. L. H., (ed.). Oxford: Pergamon Press. West, J. R. &Cotton, A. P. 1981 The measurement of diffusion coefficients in the Conwy Estuary. Estuarine, Coastal and Shelf Science 12,32>336.

Notation 2 u,v,w

Subscripts A d S

X¶ Y, 2

dye concentration (g 1~ ‘) depth of flow (m) velocities relating to x,y and z directions respectively, in a Cartesian system shear velocity (m s I three co-ordinate directions in the Cartesian co-ordinate system turbulent diffusion coefficients transverse mixing coefFicient variance of distribution in i direction

area mean value depth mean value solute transport three co-ordinate directions

in the Cartesian

co-ordinate

system

co-ordinate