Observations of the turbulent structure of a suspension of sand in a tidal current

Continental Shelf Research, Vol. 14, No. 4, pp. 429-435, 1994

Pergamon

Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0278~1343/94 $6.00 + 0.00

NOTE Observations of the turbulent structure of a suspension of sand in a tidal current R. L. SOULSBY,*'t" R. ATKINS* and A. P. SALKIELD~ (Received 22 August 1991; in revised form 4 March 1992; accepted 15 October 1992) Abstract--Measurements of the high-frequency fluctuations in the concentration of sand suspended by a tidal current, taken simultaneously with high-frequency measurements of the horizontal and vertical components of water velocity above the sandy bed of an estuary, have been used to examine the turbulent structure of the suspension, the physical mechanisms which suspend the sediment, and the damping of the turbulent kinetic energy caused by the suspension. The turbulent "bursting" phenomenon is found to play an important role in the suspension process.

INTRODUCTION

THE suspension of sand by a tidal current is a complex turbulent process, involving a two-way interaction between the flow whose turbulence produces the upward velocities necessary for suspension and the sand whose density causes a damping of the turbulence, and hence a modification of the flow. Measurements of the time averaged turbulence quantities for both the flow and the sediment in a tidal current over sandwaves were reported by SOULSBY et al. (1984, 1986). The present paper describes further highfrequency field measurements to elucidate the detailed spatial and temporal behaviour of the turbulent processes, again in a tidal current without waves. Subsequent work, in which the variation in mean and turbulent velocities and sediment concentrations over a whole sandwave were measured, was reported by ATKINS et al. (1989) and SOULSBVet al. (1991). Very detailed measurements of mean and turbulent velocity (without mobile sediments) over model sandwaves in a flume have been made by VAN DER KNAAP et al. (1991). Highfrequency measurements of velocity and sediment concentration under waves, or combined waves and currents, have been made by HANES and HUNTLEY (1986) and HANES (1990, 1991). EXPERIMENTAL

DETAILS

The measurements were made in July 1982 in a tidal flow in the Taw Estuary, North Devon, U.K. Sandwaves were present at the site, having an asymmetry aligned with the *HR Wallingford, Howbery Park, Wallingford, Oxon OXl0 8BA, U.K. tAuthor to whom correspondence should be addressed. :~SIRAD Inc, Moline, Illinois, U.S.A. 429

430

R . L . SOULSBYet al.

flood tide, which is strongly dominant at this site. Wave activity was negligible, and the water column was unstratified. The m e a s u r e m e n t s of the horizontal c o m p o n e n t , 0 + u(t), and the vertical c o m p o n e n t w(t) of water velocity were made with an electromagnetic current meter ( E M C M ) , m o u n t e d adjacent to a sand transport p r o b e (STP). This measured the instantaneous concentration of suspended sand, C + c(t), by detecting the impact rate of sand grains striking an underwater sensor. The overbar denotes a time-mean over a suitable period (12 min in our case), and the lower-case letters denote fluctuations about the mean. Both types of instrument responded to fluctuations with frequencies of up to 5 Hz. Two E M C M / S T P pairs at heights o f z = 13 and 33 cm and a third STP at z = 78 cm, were m o u n t e d above the crest o f a sandwave (25 m wavelength, 75 cm height) on an area of sand flats exposed at low tide. The m e a s u r e m e n t s were made on the ensuing flood tide once the instruments were adequately submerged, and ended at high water. The depth of water at the location of the instruments was 2.7 m at the time of m a x i m u m current and 4.8 m at high water. The suspended quartz sand had a median diameter of 165 urn, with a mean settling velocity of w~ -- 1.7 cm s -1. Details of the experiment and the analysis methods are similar to those reported by SOULSB¥ et al. (1986). RESULTS

Time series of c(t) from three STPs (Fig. 1) reveal clouds of suspended sediment separated by brief intervals of clearer water. Measurements with longer sampling times (e.g. MULDER et al., 1986) would be unable to resolve these features. Visual inspection indicates a degree of correlation between the sensors at z = 13 and 33 cm, and to a lesser extent between these and the sensor at 78 cm. Lagged cross-correlations between the sensors confirm this and also show that the m a x i m u m correlation is obtained when the lower sensors lag the u p p e r ones (Fig. 2). Autocorrelations for each sensor show that the streamwise extent of the clouds is largest near the bed and decreases upwards. After z=13crn

2500-

~_-- 2000-

1500-

g

u

1000-

500.

0

)

Time

Fig. 1.

(s)

Simultaneous concentration time series at three heights. Prominent correlated features are arrowed.

431

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0"6

-

~

ij

I Level 1 = 1 3 c m r12

~ °]

Level 2 = 3 3 c m [ Level 3 = 7 8 c m

~ y

Fig. 2.

Cross-correlations

r23

rii(Gt ) of concentration time series,

where level j lags level i by a time

interval dt.

conversion to spatial scales, a picture of the typical cloud of sand is revealed as having a horizontal extent of ~ 1 0 0 cm and a vertical extent of at least 78 cm, inclined in the downstream direction at an angle of about 60 ° to the horizontal (Fig. 3). The shape is reminiscent of the bursting events observed in the laboratory by e.g. GRASS (1983) and SUMER (1986), and the structure above the level z = 78 cm might be as conjectured in Fig. 3. The above authors have shown that at the laboratory scale the entrainment of sand grains is closely related to the turbulent bursting process. The bursting events which contribute most to the mean Reynolds stress - p u w are ejections (u < 0, w > 0) and sweeps (u > 0, w < 0). These events might also potentially contribute to the upward sediment flux 140

(z.,)

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Fig. 3.

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,"'~ J "'~ ' ' I ~" 0 20 40 oC ( c m )

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Shape of the average cloud of sediment, constructed from auto- and cross-correlation data. The shape above 78 cm is conjectural.

432

R . L . SOULSBYet al.

200I - UW(cmzs-z) °F -200 ~-

~'~!V~I !

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Fig. 4.

Simultaneous time series of uw(t) and c(t), showing clouds of high c during ejections (El, and weaker effects of sweeps (S), outward (O1) and inward (ll) interactions.

c-w, since an ejection can be envisaged as a parcel of water thrown up (w > 0) from the bed where concentrations are large (c > 0), while sweeps might carry low concentration water (c < 0) down (w < 0) towards the bed. A comparison between time series of c(t) and uw(t) (Fig. 4), demonstrates the correlation between ejections and high concentrations, but the correlation between sweeps and clearer water is less apparent. The other types of event, outward interactions (u > 0, w > 0) and inward interactions (u < 0, w < 0), do not appear to correlate with concentration. The roles of the four types of event are shown more clearly in Fig. 5, in which the method of GORDON and WITTING (1977) was used to identify the largest events which, when summed, contribute 90% to - p u w . The mean of c during all the events of a particular type occurring within 25 cm 2 s -2 bands of luwl were then calculated. Figure 5 shows that: concentrations are indeed larger than average during ejections and c increases with luw[; during sweeps the water is a little clearer than average but by an amount which does not depend on luw[; outward and inward interactions have little or no relation with c. Calculating the proportions of - p u w and U~ contributed during bursting events we find that, averaged over both heights: -

Ejections contribute 60% of - p u w and 42% of c w in 12% of the time. Sweeps contribute 56% of - p u w and 23% of ~ in 11% of the time. OIs contribute - 1 5 % of - p u w and 3% of cn---;in 3% of the time. IIs contribute - 1 1 % o f - p u w and 1% of ~ in 3% of the time. The remaining 10% of - p u w and 31% of c-w are contributed by non-events, which occupy 71% of the time. The result for c w is more remarkable than that for - p u w , since the criterion for selecting events is based only on their contribution to uw. It confirms that ejections are the dominant mechanism for the suspension of sand; by contrast sweeps are the dominant mechanism for bedload movement of sediment (HEATHERSHAW and THORNE, 1985). AS the sand grains are lifted by the ejections their potential energy increases. During viscous settling of the grains back to the bed this potential energy is dissipated as heat. The turbulent kinetic energy k = ½p(u 2 + v 2 + w 2) of the flow is thus reduced by the suspension

433

The turbulent structure of a sand suspension

500

500

I z=33cm O= (33)=116cm S400

400

300

300

200

200

100 c (mg 1-1)

100

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160

~0

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Fig. 5.

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The concentration associated with different types of event, as a function of the amplitnde ]uwl of the event.

process. This process is analogous to mixing of a thermally stratified atmospheric boundary layer, and a parameter equivalent to the atmospheric M o n i n - O b u k h o v stability parameter can be defined by = gKZ(ps -- p)Cw~ PPs(--~)3/2 '

(1)

where g is the acceleration due to gravity, K = 0.40 is von Karman's constant, and p and p, are the densities of water and sediment material, respectively. We do not have simultaneous measurements of u, v and w in order to calculate k, but we can plot individual components against ~ as in Fig. 6, in which t h e p r e s e n t data is supplemented by that described in SOVLSBVet al. (1984). The values of U are taken at the same height as the corresponding (~)1/2. As ~ increases, ( u 2 ) m / U decreases until ~ ~ 0.1, then levels off at a value of about 1/2 of the sediment-free value. The other components, v and w, behave similarly. Thus k / ( l 2 would be reduced to about a quarter of the sediment-free value. This effect can alternatively be viewed as being due to an increase in /] for a given turbulence-level, due to drag-reduction when sediment is in suspension. CONCLUSIONS

From measurements of the high-frequency fluctuations in water velocity and suspended sand concentration near the bed of a tidal estuary we find: (a) that suspended sand travels as clouds which correlate over horizontal and vertical distances of order 100 cm, and lean downstream; (b) that these correlate well with the ejection events of the turbulent bursting process, while sweeps correlate weakly with clearer water; (c) that, together, ejections and sweeps account for 65% of the flux c--~ of sediment in only 23% of the time;

434

R . L . SOULSBYet al.

0.3

• TAWS0 z=18cm • TAW82 z=33cm 7 TAW82 z=13crn

02

01

ol o

52

54

~+

•

v • ~7 & &

~8

~o

• •

.n'VA

~2

i'4

v

V

v

~

1~

~0

~2

2~

Fig. 6. Damping of the u-component of turbulence intensity causedby suspendedsediment. Data labelled T A W 82 is from the present experiment, that labelled T A W 80 is from SOULSBY el a/. (1984).

(d) that when sand is suspended the relative turbulent kinetic energy of the flow is reduced to as little as a quarter of the sediment-free value. Acknowledgements--We thank Mrs B. Wainwright and Mr N. Oliver who undertook some of the computations. The experiment was performed while R. L. Soulsby and A. P. Salkield were working at the former Institute of Oceanographic Sciences T a u n t o n Laboratory. Much of the analysis and interpretation were undertaken at H R Wallingford. The work was funded by the U.K. D e p a r t m e n t of the Environment.

REFERENCES

SOULSBY,C. B. WATERSand N. ()LIVER (1989) Field measurements of sediment su~spension above bedforms in a sandy estuary. Hydraulics Research, Report SR 203, 21pp. GORDON C. M. and J. W]TnN6 (1977) Turbulent structure in a benthic boundary layer. In: Bottom turbulence, ATKINS R., R. L.

J. C. J. NIHOUL, editor, Elsevier, A m s t e r d a m , pp. 59-81. GRASS A. J. (1983) The influence of boundary layer turbulence on the mechanics of sediment transport. In: Proceedings of Euromech 156, Mechanics of Sediment Transport+ B. M. SUMER and A. MULI,ER, editors, Balkema, Rotterdam, pp. 3-17. HANES D. M. (1990) The structure of events of intermittent suspension of sand due to shoaling waves. In: The Sea+ Vol. 9, B. LE MEHAUT~ and D. M. HANES, editors, John Wiley and Sons, New York, pp. 941-952. HANES D. M. (1991) Suspension of sand due to wave groups. Journal of Geophysical Research, 96(C5), 8911 8915. HANES D. M. and D. A. HUNTLEY (1986) Continuous m e a s u r e m e n t s of suspended sand concentration in a wave dominated nearshore environment. Continental Shelf Research, 6(4), 585-596. HEATHERSHAWA. D. and P. D. THORNE (1985) Sea bed noises reveal role of turbulent bursting p h e n o m e n o n in sediment transport by tidal currents. Nature, 316, 339-342. MULDER H. P. J., L. H. M. KOHSIEK and A. C. VAN DER KOLK (1986) Turbulence in terms of coherent structures and their relation to sand concentration in tidal channels. In: Proceedings of' Euromech 192, Transport of Suspended Solids in Open Channels, W. BECHTELER, editor, Balkema, Rotterdam, pp, 187-194. SOULSBYR. L., R. ATKINS, C. B. WATERS and N. OLIVER (1991) Field m e a s u r e m e n t s of suspended sediment over sandwaves. In: Proceedings of Euromech 262, Sand Transport in Rivers, Estuaries and the Sea, R. L. SOULSBY and R. BETrESS, editors, Balkema, R o t t e r d a m , pp. 155-162.

The turbulent structure of a sand suspension

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SOULSBY R. L., A. P. SALKIELD,R. A. HAINE and B. WAINWRIGHT(1986) Observations of the turbulent fluxes of s u s p e n d e d sand near the sea bed. In: Proceedings of Euromech 192, Transport of Suspended Solids in ()pen Channels, W. BECHTELER, editor, Balkema, R o t t e r d a m , pp. 183-186. SOULSBYR. L,, A. P. SALKIELDand G. P. LE GOOD (1984) M e a s u r e m e n t s of the turbulence characteristics of sand s u s p e n d e d by a tidal current. Continental Shelf Research, 3, 439-454. SUMER B. M. (1986) Recent developments on the mechanics of sediment suspension. Proceedings of Euromech 192, Transport of Suspended Solids in Open Channels, W. BECHTELER, editor, Balkema, Rotterdam, pp. 3 13. VAN DER KNAAP F. C. M., M. C. L. M. VAN MIERLO and M. J. OFFICIER (1991) M e a s u r e m e n t s and computations of the turbulent flow field above fixed bed-forms. In: Proceedings of Euromech 262, Sand Transport in Rivers, Estuaries and the Sea, R. L. SOULSBYand R. BEaO'ESS, editors, Balkema, Rotterdam. pp. 179-185.