Length and Time Scales of Response of Sediment Suspensions to Changing Flow Conditions
Publication: Journal of Hydraulic Engineering
Volume 138, Issue 5
Abstract
Turbulent suspensions of sediment are investigated to establish the characteristic length and time scales on which they adjust from one state to another. The suspensions are modeled by using a simple closure for the turbulent fluctuations in which the average flux of sediment is treated as a diffusion process. A key dimensionless settling parameter, which is closely related to the Rouse number, measures the magnitude of the settling to diffusive fluxes of particles. It is shown how the length and time scales on which the suspension responds are a function of the settling parameter and the assumed form of the eddy diffusivity, and that the predictions are broadly in accord with laboratory experiments. It is further established analytically that, in the regimes of the settling parameter much greater or much less than unity, the timescale of response is independent of the form of the eddy diffusivity. This motivates the use of simple eddy diffusivity laws to provide generic insight to the unsteady evolution of complex suspension and sedimentation problems.
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Acknowledgments
This work was supported by the Natural Environment Research Council under grant number (NER/S/A/2006/14067). The authors thank David Pritchard for a constructive critique of the work and informative comments. The authors also thank three anonymous referees for their reviews, which significantly improved this work.
References
Apmann, R. P., and Rumer, R. R. (1970). “Diffusion of sediment in developing flow.” J. Hydraul. Division, 96(HY1), 109–123.
Ashida, K., and Okabe, T. (1982). “On the calculation method of the concentration of suspended sediment under non-equilibrium condition.” Proc. 26th Conference on Hydraulics JSCE (in Japanese), 153–158.
Cao, Z., and Carling, P. A. (2002). “Mathematical modelling of alluvial rivers: Reality and myth. Part 2: Special issues.” Proceedings of the ICE - Water and Maritime Engineering, Institution of Civil Engineers (ICE), London, 154(4), 297–307.
Celic, I., and Rodi, W. (1988). “Modelling suspended sediment transport in nonequilibrium situations.” J. Hydr. Eng., 114(10), 1157–1191.
Claudin, P., Charru, F., and Andreoti, B. (2011). “Transport relaxation time and length scales in turbulent suspensions.” J. Fluid Mech., 671, 491–506.JFLSA7
Drew, D. A. (1983). “Mathematical modeling of two-phase flow.” Annu. Rev. Fluid Mech., 15, 261–291.ARVFA3
Dyer, K. R., and Soulsby, R. L. (1988). “Sand transport on the continental shelf.” Annu. Rev. Fluid Mech.ARVFA3, 20, 295–324.
Fredsoe, J., and Deigaard, R. (1992). Mechanics of coastal sediment transport, World Scientific, Singapore.
Hinch, E. J. (1992). Perturbation methods, Cambridge University Press, Cambridge, United Kingdom.
Hjelmfelt, A. T., and Lenau, C. W. (1970). “Nonequilibrium transport of suspended sediment.” J. Hydraul. Div.JYCEAJ, 96(7), 1567–1586.
Hsu, T. J., Jenkins, J. T., and Liu, P. L. F. (2004). “On two-phase sediment transport: Sheet flow of massive particles.” Proc. R. Soc. London, Ser. APRLAAZ, 460(2048), 2223–2250.
Huijts, K. M. H., Schuttelaars, H. M., de Swart, H. E., and Valle-Levinson, A. (2006). “Lateral entrapment of sediment in tidal estuaries: An idealised model study.” J. Geophys. Res., 111(C12), C12016–C12029,.JGREA2
Jenkins, J. T., and Hanes, D. M. (1998). “Collisional sheet flows of sediment driven by a turbulent fluid.” J. Fluid Mech., 370(x), 29–52.JFLSA7
Jobson, H. E., and Sayre, W. W. (1970a). “Predicting concentration profiles in open channels.” J. Hydraul. Div.JYCEAJ, 96(10), 1983–1996.
Jobson, H. E., and Sayre, W. W. (1970b). “Vertical transfer in open channel flow.” J. Hydraul. Div.JYCEAJ, 96(3), 703–724.
MatLab Version 7.1 [Computer software]. The MathWorks, Inc., Natick, MA.
Mei, C. C. (1969). “Nonuniform diffusion of suspended sediment.” J. Hydraul. Div.JYCEAJ, 95(1), 581–584.
Prandle, D. (1997). “Tidal characteristics of suspended sediment concentrations.” J. Hydraul. Eng.JHEND8, 123(4), 341–350.
Pritchard, D. (2006). “Rate of deposition of fine sediment from suspension.” J. Hydraul. Eng.JHEND8, 132(5), 533–536.
Pritchard, D., and Hogg, A. J. (2002). “On sediment transport under dam-break flow.” J. Fluid Mech.JFLSA7, 473, 265–274.
Rouse, H. (1938). “Experiments on the mechanics of sediment suspensions.” Proc. 5th Int. Congress for Applied Mechanics, Vol 55, Wiley, New York, 550–554.
Soulsby, R. L. (1998). Dynamics of marine sands, Thomas Telford, London.
Stansby, P. K., and Awang, M. A. O. (1998). “Response time analysis for suspended sediment transport.” J. Hydraul. Res.JHYRAF, 36(3), 327–338.
Sumner, E. J., Amy, L. A., and Talling, P. J. (2008). “Deposits structure and processes of sand deposition from decelerating sediment suspensions.” J. Sediment. Res., 78(8), 529–547.JSERFV
Tu, H., Tamai, N., and Kawahara, Y. (1993). “Diffusion of suspended load in unsteady open-channel flow.” JSCE Proc. Hydraulic Engineering, 37, 373–378.
van Rijn, L. C. (1984a). “Sediment pick-up functions.” J. Hydraul. Eng., 110(10), 1494–1502.
van Rijn, L. L. (1984b). “Sediment transport, Part 2: Suspended load transport.” J. Hydraul. Eng.JHEND8, 110(11), 1613–1641.
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© 2012. American Society of Civil Engineers.
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Received: Apr 4, 2011
Accepted: Nov 10, 2011
Published online: Nov 12, 2011
Published in print: May 1, 2012
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