Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-25T11:52:57.664Z Has data issue: false hasContentIssue false
  • English
  • Français

Streamwise streaks induced by bedload diffusion

Published online by Cambridge University Press:  25 January 2019

Anaïs Abramian Open the ORCID record for Anaïs Abramian [Opens in a new window] ,
Olivier Devauchelle  and
Eric Lajeunesse
Anaïs Abramian*
Affiliation:
Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris-Diderot, UMR 7154 CNRS, 1 rue Jussieu, 75238 Paris CEDEX 05, France
Olivier Devauchelle
Affiliation:
Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris-Diderot, UMR 7154 CNRS, 1 rue Jussieu, 75238 Paris CEDEX 05, France
Eric Lajeunesse
Affiliation:
Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris-Diderot, UMR 7154 CNRS, 1 rue Jussieu, 75238 Paris CEDEX 05, France
*
†Email address for correspondence: anaisabramian@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

A fluid flowing over a granular bed can move its superficial grains, and eventually deform it by erosion and deposition. This coupling generates a beautiful variety of patterns, such as ripples, bars and streamwise streaks. Here, we investigate the latter, sometimes called ‘sand ridges’ or ‘sand ribbons’. We perturb a sediment bed with sinusoidal streaks, the crests of which are aligned with the flow. We find that, when their wavelength is much larger than the flow depth, bedload diffusion brings mobile grains from troughs, where they are more numerous, to crests. Surprisingly, gravity can only counter this destabilising mechanism when sediment transport is intense enough. Relaxing the long-wavelength approximation, we find that the cross-stream diffusion of momentum mitigates the influence of the bed perturbation on the flow, and even reverses it for short wavelengths. Viscosity thus opposes the diffusion of entrained grains to select the most unstable wavelength. This instability might turn single-thread alluvial rivers into braided channels.

JFM classification

Granular media: Granular media Geophysical and Geological Flows: Sediment transport
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 601 - 619
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, J. R. L. 1982 Sedimentary Structures, Their Character and Physical Basis, vol. 1. Elsevier.Google Scholar
Andreotti, B., Claudin, P., Devauchelle, O., Durán, O. & Fourrière, A. 2012 Bedforms in a turbulent stream: ripples, chevrons and antidunes. J. Fluid Mech. 690, 94–128.10.1017/jfm.2011.386Google Scholar
Aussillous, P., Chauchat, J., Pailha, M., Médale, M. & Guazzelli, E. 2013 Investigation of the mobile granular layer in bedload transport by laminar shearing flows. J. Fluid Mech. 736, 594–615.10.1017/jfm.2013.546Google Scholar
Aussillous, P., Zou, Z., Guazzelli, É., Yan, L. & Wyart, M. 2016 Scale-free channeling patterns near the onset of erosion of sheared granular beds. Proc. Natl Acad. Sci. USA, 201609023.10.1073/pnas.1609023113Google Scholar
Bagnold, R. 1973 The nature of saltation and of bedload transport in water. Proc. R. Soc. Lond. A 332, 473–504.10.1098/rspa.1973.0038Google Scholar
Bernal, J. D. & Mason, J. 1960 Packing of spheres: co-ordination of randomly packed spheres. Nature 188 (4754), 910–911.10.1038/188910a0Google Scholar
Charru, F. 2006 Selection of the ripple length on a granular bed sheared by a liquid flow. Phys. Fluids 18 (12), 121508.10.1063/1.2397005Google Scholar
Charru, F., Andreotti, B. & Claudin, P. 2013 Sand ripples and dunes. Annu. Rev. Fluid Mech. 45, 469–493.10.1146/annurev-fluid-011212-140806Google Scholar
Charru, F., Mouilleron, H. & Eiff, O. 2004 Erosion and deposition of particles on a bed sheared by a viscous flow. J. Fluid Mech. 519, 55–80.10.1017/S0022112004001028Google Scholar
Chen, X., Ma, J. & Dey, S. 2009 Sediment transport on arbitrary slopes: simplified model. J. Hydraulic Engng 136 (5), 311–317.10.1061/(ASCE)HY.1943-7900.0000175Google Scholar
Coleman, S. E. & Melville, B. W. 1994 Bed-form development. J. Hydraulic Engng 120 (5), 544–560.10.1061/(ASCE)0733-9429(1994)120:5(544)Google Scholar
Colombini, M. 1993 Turbulence-driven secondary flows and formation of sand ridges. J. Fluid Mech. 254, 701–719.10.1017/S0022112093002319Google Scholar
Colombini, M. & Parker, G. 1995 Longitudinal streaks. J. Fluid Mech. 304, 161–183.10.1017/S0022112095004381Google Scholar
Colombini, M., Seminara, G. & Tubino, M. 1987 Finite-amplitude alternate bars. J. Fluid Mech. 181, 213–232.10.1017/S0022112087002064Google Scholar
Devauchelle, O., Malverti, L., Lajeunesse, E., Josserand, C., Lagrée, P. Y. & Métivier, F. 2010 Rhomboid beach pattern: a laboratory investigation. J. Geophys. Res. 115, F02017.10.1029/2009JF001471Google Scholar
Einstein, H. A. 1937 Bed load transport as a probability problem. In Sedimentation: 746 Symposium to Honor Professor H.A. Einstein, 1972. translation from 747 German of H. A. Einstein doctoral thesis. Originally presented to Federal Institute of Technology, Zurich, Switzerland, 1937, pp. C1–C105. Zurich.Google Scholar
Exner, F. M. 1925 Uber die wechselwirkung zwischen wasser und geschiebe in flussen. Akad. Wiss Wien, Math-Naturwissensch. Klasse, Sitzungsber., Abt. IIa 134, 165–203.Google Scholar
Furbish, D. J., Haff, P. K., Roseberry, J. C. & Schmeeckle, M. W. 2012 A probabilistic description of the bed load sediment flux: 1. Theory. J. Geophys. Res. 117 (F3), F03031.Google Scholar
Ikeda, S., Parker, G. & Kimura, Y. 1998 Stable width and depth of straight gravel rivers with heterogeneous bed materials. Water Resour. Res. 24, 713–722.10.1029/WR024i005p00713Google Scholar
Karcz, I. 1967 Harrow marks, current-aligned sedimentary structures. J. Geology 75 (1), 113–121.10.1086/627235Google Scholar
Kennedy, John F. 1963 The mechanics of dunes and antidunes in erodible-bed channels. J. Fluid Mech. 16 (4), 521–544.10.1017/S0022112063000975Google Scholar
Kovacs, A. & Parker, G. 1994 A new vectorial bedload formulation and its application to the time evolution of straight river channels. J. Fluid Mech. 267, 153–183.10.1017/S002211209400114XGoogle Scholar
Lajeunesse, E., Malverti, L. & Charru, F. 2010 Bedload transport in turbulent flow at the grain scale: experiments and modeling. J. Geophys. Res. Earth Surf. 115, F04001.10.1029/2009JF001628Google Scholar
Lobkovsky, A. E., Orpe, A. V., Molloy, R., Kudrolli, A. & Rothman, D. H. 2008 Erosion of a granular bed driven by laminar fluid flow. J. Fluid Mech. 605 (1), 47–58.10.1017/S0022112008001389Google Scholar
McLelland, S. J., Ashworth, P. J., Best, J. L. & Livesey, J. R. 1999 Turbulence and secondary flow over sediment stripes in weakly bimodal bed material. J. Hydraulic Engng 125 (5), 463–473.10.1061/(ASCE)0733-9429(1999)125:5(463)Google Scholar
Métivier, F., Lajeunesse, E. & Devauchelle, O. 2017 Laboratory rivers: Lacey’s law, threshold theory, and channel stability. Earth Surf. Dyn. 5 (1), 187–198.10.5194/esurf-5-187-2017Google Scholar
Meyer-Peter, E. & Müller, R. 1948 Formulas for bed-load transport. In Proceedings, 2nd Congress, International Association of Hydraulic Research (ed. Sweden, Stockholm), pp. 39–64. International Association of Hydraulic Research.Google Scholar
Nikora, V., Habersack, H., Huber, T. & McEwan, I. 2002 On bed particle diffusion in gravel bed flows under weak bed load transport. Water Resour. Res. 38 (6), 1081.10.1029/2001WR000513Google Scholar
Ouriemi, M., Aussillous, P. & Guazzelli, E. 2009 Sediment dynamics. Part 1. Bed-load transport by laminar shearing flows. J. Fluid Mech. 636, 295–319.10.1017/S0022112009007915Google Scholar
Ouriemi, M., Aussillous, P., Medale, M., Peysson, Y. & Guazzelli, É. 2007 Determination of the critical Shields number for particle erosion in laminar flow. Phys. Fluids 19 (6), 061706.10.1063/1.2747677Google Scholar
Parker, G. 1976 On the cause and characteristic scales of meandering and braiding in rivers. J. Fluid Mech. 76 (3), 457–480.10.1017/S0022112076000748Google Scholar
Seizilles, G., Lajeunesse, E., Devauchelle, O. & Bak, M. 2014 Cross-stream diffusion in bedload transport. Phys. Fluids 26 (1), 013302.10.1063/1.4861001Google Scholar
Seminara, G. 2010 Fluvial sedimentary patterns. Annu. Rev. Fluid Mech. 42, 43–66.10.1146/annurev-fluid-121108-145612Google Scholar
Shields, A. S.1936 Anwendung der aehnlichkeitsmechanik und der turbulenzforschung auf die geschiebebewegung. PhD thesis, Technical University Berlin, Germany. Preussischen Versuchsanstalt für Wasserbau.Google Scholar
Stebbings, J. 1963 The shapes of self-formed model alluvial channels. Proc. Inst. Civ. Engrs 25 (4), 485–510.Google Scholar
Vanderwel, C. & Ganapathisubramani, B. 2015 Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers. J. Fluid Mech. 774, R2.10.1017/jfm.2015.292Google Scholar
Willingham, D., Anderson, W., Christensen, K. T. & Barros, J. M. 2014 Turbulent boundary layer flow over transverse aerodynamic roughness transitions: induced mixing and flow characterization. Phys. Fluids 26 (2), 025111.10.1063/1.4864105Google Scholar
Yamasaka, M., Ikeda, S. & Kizaki, S. 1987 Lateral sediment transport of heterogeneous bed materials. Doboku Gakkai Ronbunshu 1987 (387), 105–114.10.2208/jscej.1987.387_105Google Scholar