Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-10T15:07:18.915Z Has data issue: false hasContentIssue false
  • English
  • Français

Transport relaxation time and length scales in turbulent suspensions

Published online by Cambridge University Press:  11 February 2011

PHILIPPE CLAUDIN ,
FRANÇOIS CHARRU  and
BRUNO ANDREOTTI
PHILIPPE CLAUDIN*
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR 7636 ESPCI–CNRS, Université Paris Diderot–Université Pierre et Marie Curie, 10 rue Vauquelin, 75005 Paris, France
FRANÇOIS CHARRU
Affiliation:
Institut de Mécanique des Fluides de Toulouse–CNRS, Université de Toulouse, 31400 Toulouse, France
BRUNO ANDREOTTI
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR 7636 ESPCI–CNRS, Université Paris Diderot–Université Pierre et Marie Curie, 10 rue Vauquelin, 75005 Paris, France
*
†Email address for correspondence: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that in a turbulent flow transporting suspended sediment, the unsaturated sediment flux q(x, t) can be described by a first-order relaxation equation. From a mode analysis of the advection–diffusion equation for the particle concentration, the relaxation length and time scales of the dominant mode are shown to be the deposition length HU/Vfall and deposition time H/Vfall, where H is the flow depth, U the mean flow velocity and Vfall the sediment settling velocity. This result is expected to be particularly relevant for the case of sediment transport in slowly varying flows, where the flux is never far from saturation. Predictions are shown to be in quantitative agreement with flume experiments, for both net erosion and net deposition situations.

JFM classification

Geophysical and Geological Flows: Sediment transport Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 671 , 25 March 2011 , pp. 491 - 506
Copyright
Copyright © Cambridge University Press 2011. The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution-NonCommercial-ShareAlike licence <http://creativecommons.org/licenses/by-nc-sa/2.5/>. The written permission of Cambridge University Press must be obtained for commercial re-use.

References

REFERENCES

Andreotti, B. 2004 A two species model of aeolian sand transport. J. Fluid Mech. 510, 47–50.CrossRefGoogle Scholar
Andreotti, B., Claudin, P. & Douady, S. 2002 Selection of dune shapes and velocities. Eur. J. Phys. B 28, 341.CrossRefGoogle Scholar
Apmann, R. P. & Rumer, R. R. 1970 Diffusion of sediment in developing flow. J. Hydraul. Div. ASCE 96, 109–123.CrossRefGoogle Scholar
Ashida, K. & Okabe, T. 1982 On the calculation method of the concentration of suspended sediment under non-equilibrium condition (in Japanese). In Proceedings of the 26th Conference on Hydraulics, pp. 153–158. JSCE.Google Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2007 Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98, 084502.CrossRefGoogle ScholarPubMed
Bonelli, S., Brivois, O. & Benahmed, N. 2007 Modélisation du renard hydraulique et interprétation de l'essai d'érosion de trou. Rev. Fr. Geotech. 118, 13–22.CrossRefGoogle Scholar
Briaud, J. L., Ting, F. C. K., Chen, H. C., Cao, Y., Han, S. W. & Kwak, K. W. 2001 Erosion function apparatus for scour rate predictions. J. Geotech. Geoenviron. Engng 127, 105–113.CrossRefGoogle Scholar
Celik, I. & Rodi, W. 1988 Modeling suspended sediment transport in nonequilibrium situations. J. Hydraul. Engng 114, 1157–1191.CrossRefGoogle Scholar
Charru, F. 2006 Selection of the ripple length on a granular bed sheared by a liquid flow. Phys. Fluids 18, 121508.CrossRefGoogle Scholar
Coleman, N. L. 1970 Flume studies of the sediment transfer coefficient. Water Resour. Res. 6, 801–809.CrossRefGoogle Scholar
Davy, P. & Lague, D. 2009 Fluvial erosion/transport equation of landscape evolution models revisited. J. Geophys. Res. 114, F03007.Google Scholar
Einstein, H. A. 1950 The bedload function for sediment transportation in open channel flow. Tech. Bull. 1026, pp. 1–71. US Department of Agriculture.Google Scholar
Engelund, F. 1970 Instability of erodible beds. J. Fluid Mech. 42, 225–244.CrossRefGoogle Scholar
Fourrière, A., Claudin, P. & Andreotti, B. 2010 Bedforms in a turbulent stream: formation of ripples by primary linear instability and of dunes by non-linear pattern coarsening. J. Fluid Mech. 649, 287–328.CrossRefGoogle Scholar
Fredsøe, J. & Deigaard, R. 1992 Mechanics of Coastal Sediment Transport. World Scientific.CrossRefGoogle Scholar
Hanson, G. J. & Simon, A. 2001 Erodibility of cohesive streambeds in the loess area of the midwestern USA. Hydraul. Process. 15, 23–38.CrossRefGoogle Scholar
Hjelmfelt, A. T. & Lenau, C. W. 1970 Nonequilibrium transport of suspended sediment. J. Hydraul. Div. ASCE 96, 1567–1586.CrossRefGoogle Scholar
Hunt, J. C. R., Delfos, R., Eames, I. & Perkins, R. 2007 Vortices, complex flows and inertial particles. Flow Turbul. Combust. 79, 207–234.CrossRefGoogle Scholar
Jobson, A. E. & Sayre, W. W. 1970 Vertical transfer in open channel flow. J. Hydraul. Div. ASCE 96, 703–724.CrossRefGoogle Scholar
Kroy, K., Sauermann, G. & Herrmann, H. J. 2002 Minimal model for aeolian sand dunes. Phys. Rev. E 66, 031302.CrossRefGoogle ScholarPubMed
Lajeunesse, E., Malverti, L. & Charru, F. 2010 Bedload transport in turbulent flow at the grain scale: experiments and modeling. J. Geophys. Res. 115, F04001.Google Scholar
Mei, C. C. 1969 Nonuniform diffusion of suspended sediment. J. Hydraul. Div. ASCE 95, 581–584.CrossRefGoogle Scholar
Nezu, I. 2005 Open-channel flow turbulence and its research prospect in the 21st century. J. Hydraul. Engng 131, 229–246.CrossRefGoogle Scholar
Nezu, I. & Rodi, W. 1986, Open-channel flow measurements with a laser doppler anemometer. J. Hydraul. Engng. 112, 335–355.CrossRefGoogle Scholar
Nielsen, P. 1992 Coastal Bottom Boundary Layers and Sediment Transport. World Scientific.CrossRefGoogle Scholar
Ouillon, S. & Le Guennec, B. 1996 Modelling non-cohesive suspended sediment transport in 2D vertical free surface flows. J. Hydraul. Res. 34, 219–236.CrossRefGoogle Scholar
Parker, G. 1978 Self-formed straight rivers with equilibrium banks and mobile bed. Part 1. The sand–silt river. J. Fluid Mech. 89, 109–125.CrossRefGoogle Scholar
Raudkivi, A. J. 1998 Loose Boundary Hydraulics. A. A. Balkema.Google Scholar
van Rijn, L. C. 1984 a Sediment pick-up functions. J. Hydraul. Engng 110, 1494–1502.CrossRefGoogle Scholar
van Rijn, L. C. 1984 b Sediment transport. Part II. Suspended load transport. J. Hydraul. Engng 110, 1613–1641.CrossRefGoogle Scholar
van Rijn, L. C. 1986 a Application of sediment pickup function. J. Hydraul. Engng 112, 867–874.CrossRefGoogle Scholar
van Rijn, L. C. 1986 b Mathematical modeling of suspended sediment in nonuniform flows. J. Hydraul. Engng 112, 433–455.CrossRefGoogle Scholar
Rouse, H. 1936 Modern conceptions of the mechanics of fluid turbulence. Trans. ASCE 102, 463–543.Google Scholar
Sauermann, G., Kroy, K. & Herrmann, H. J. 2001 A phenomenological dynamic saltation model for dune formation. Phys. Rev. E 64, 031305.CrossRefGoogle Scholar
Seminara, G. 2006 Meanders. J. Fluid Mech. 554, 271–297.CrossRefGoogle Scholar
Shields, A. 1936 Application of similarity principles and turbulence research to bed-load movement. Mitteilungen der Preussischen Versuchsanstalt für Wasserbau und Schiffbau (ed. Ott, W.D. & von Uchelen, C.), vol. 26, pp. 5–24. Soil Conservation Service, California Institute of Technology.Google Scholar
Vanoni, V. A. 1946 Transportation of suspended sediment by water. Trans. ASCE 111, 67–133.Google Scholar
Yalin, K. S. & Finlaysen, G. D. 1973 On the development of the distribution of suspended load. In Proceedings of the 15th IAHR Congress, Istanbul (ed. S. Okyay), pp. 287–294.Google Scholar