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Incipient bedforms in a bidirectional wind regime

Published online by Cambridge University Press:  14 January 2019

Cyril Gadal Open the ORCID record for Cyril Gadal [Opens in a new window] ,
Clément Narteau Open the ORCID record for Clément Narteau [Opens in a new window] ,
Sylvain Courrech du Pont ,
Olivier Rozier Open the ORCID record for Olivier Rozier [Opens in a new window]  and
Philippe Claudin Open the ORCID record for Philippe Claudin [Opens in a new window]
Cyril Gadal*
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
Clément Narteau
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
Sylvain Courrech du Pont
Affiliation:
Laboratoire Matière et Systèmes Complexes, Sorbonne Paris Cité, Université Paris-Diderot, UMR 7057 CNRS, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75205 Paris CEDEX 13, France
Olivier Rozier
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
Philippe Claudin
Affiliation:
Physique et Mécanique des Milieux Hétérogènes, PMMH UMR 7636 CNRS, ESPCI PSL Research University, Sorbonne Université, Sorbonne Paris Cité, 10 rue Vauquelin, 75005 Paris, France
*
†Email address for correspondence: gadal@ipgp.fr
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Abstract

Most terrestrial sand seas form at ‘horse’ latitudes, where the wind direction exhibits seasonal variation. Here, we extend the two-dimensional linear stability analysis of a flat sand bed associated with a unidirectional wind to the three-dimensional case in order to account for multidirectional wind regimes. Focusing on the simplest case of bidirectional flow regimes, we show that the transition from transverse to oblique or longitudinal patterns is controlled by the transport ratio and the divergence angle between the two flows. Our predictions agree with previous results for dune orientation, and also provide a wider range of possible alignments depending on flow strength, especially when the two winds are perpendicular, at which the transition occurs. This analysis also predicts the selected pattern wavelength, which either decreases close to the transition angle for strong winds, due to a geometric effect, or increases at low winds, when the bed slope affects the transport. This theoretical analysis is complemented by analogous subaqueous experiments, where bedforms are submitted to alternate water flows. For transverse bedforms, the experimental data validate the model at strong flows, providing evidence for the predicted geometric effect, but also for the increase of the wavelength close to the transport threshold. For longitudinal bedforms, a discrepancy is observed, which we interpret as the sign of enhanced nonlinearities induced by the development of slip faces when the flow alternately blows on both sides of the dune.

JFM classification

Geophysical and Geological Flows: Sediment transport
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 490 - 516
Copyright
© 2019 Cambridge University Press 

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References

Andreotti, B. 2004 A two-species model of aeolian sand transport. J. Fluid Mech. 510, 47–70.Google Scholar
Andreotti, B., Claudin, P., Devauchelle, O., Durán, O. & Fourrière, A. 2012a Bedforms in a turbulent stream: ripples, chevrons and antidunes. J. Fluid Mech. 690, 94–128.Google Scholar
Andreotti, B., Claudin, P. & Douady, S. 2002a Selection of dune shapes and velocities. Part 1. Dynamics of sand, wind and barchans. Eur. Phys. J. B 28, 321–339.Google Scholar
Andreotti, B., Claudin, P. & Douady, S. 2002b Selection of dune shapes and velocities. Part 2. A two-dimensional modelling. Eur. Phys. J. B 28, 341–352.Google Scholar
Andreotti, B., Claudin, P. & Pouliquen, O. 2010 Measurements of the aeolian sand transport saturation length. Geomorphology 123, 343–348.Google Scholar
Andreotti, B., Forterre, Y. & Pouliquen, O. 2012b Les Milieux Granulaires-Entre Fluide et Solide: Entre Fluide et Solide. EDP Sciences.Google Scholar
Baas, A. C. W. & Nield, J. M. 2007 Modelling vegetated dune landscapes. Geophys. Res. Lett. 34, L06405.Google Scholar
Baddock, M. C., Livingstone, I. & Wiggs, G. F. S. 2007 The geomorphological significance of airflow patterns in transverse dune interdunes. Geomorphology 87, 322–336.Google Scholar
Bagnold, R. A. 1941 The Physics of Wind Blown Sand and Desert Dunes. Methuen.Google Scholar
Bagnold, R. A. 1956 The flow of cohesionless grains in fluids. Phil. Trans. R. Soc. Lond. A 249, 235–297.Google Scholar
Belcher, S. E. & Hunt, J. C. R. 1998 Turbulent flow over hills and waves. Annu. Rev. Fluid Mech. 30, 507–538.Google Scholar
Charru, F., Andreotti, B. & Claudin, P. 2013 Sand ripples and dunes. Annu. Rev. Fluid Mech. 45, 469–493.Google Scholar
Claudin, P. & Andreotti, B. 2006 A scaling law for aeolian dunes on Mars, Venus, Earth, and for subaqueous ripples. Earth Planet. Sci. Lett. 252, 30–44.Google Scholar
Claudin, P., Wiggs, G. F. S. & Andreotti, B. 2013 Field evidence for the upwind velocity shift at the crest of low dunes. Boundary-Layer Meteorol. 148, 195–206.Google Scholar
Courrech du Pont, S. 2015 Dune morphodynamics. C. R. Phys. 16, 118–138.Google Scholar
Courrech du Pont, S., Narteau, C. & Gao, X. 2014 Two modes for dune orientation. Geology 42, 743–746.Google Scholar
Creyssels, M., Dupont, P., Ould El Moctar, A., Valance, A., Cantat, I., Jenkins, J. T., Pasini, J. M. & Rasmussen, K. R. 2009 Saltating particles in a turbulent boundary layer: experiment and theory. J. Fluid Mech. 625, 47–74.Google Scholar
Day, M. & Kocurek, G. 2018 Pattern similarity across planetary dune fields. Geology 46, 999–1002.Google Scholar
Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M. A., Balsamo, G., Bauer, P. et al. 2011 The era-interim reanalysis: configuration and performance of the data assimilation system. Q. J. R. Meteorol. Soc. 137, 553–597.Google Scholar
Devauchelle, O., Malverti, L., Lajeunesse, E., Lagrée, P.-Y., Josserand, C. & Nguyen Thu-Lam, K.-D. 2010 Stability of bedforms in laminar flows with free surface: from bars to ripples. J. Fluid Mech. 642, 329–348.Google Scholar
Dey, S. 2003 Threshold of sediment motion on combined transverse and longitudinal sloping beds. J. Hydraul. Res. 41, 405–415.Google Scholar
Durán, O., Andreotti, B. & Claudin, P. 2012 Numerical simulation of turbulent sediment transport, from bed load to saltation. Phys. Fluids 24, 103306.Google Scholar
Durán, O., Claudin, P. & Andreotti, B. 2011 On aeolian transport: grain-scale interactions, dynamical mechanisms and scaling laws. Aeolian Res. 3, 243–270.Google Scholar
Eastwood, E., Nield, J. M., Baas, A. & Kocurek, G. 2011 Modelling controls on aeolian dune-field pattern evolution. Sedimentology 58, 1391–1406.Google Scholar
Elbelrhiti, H., Andreotti, B. & Claudin, P. 2008 Barchan dune corridors: field characterization and investigation of control parameters. J. Geophys. Res. Earth Surf. 113, F02S15.Google Scholar
Elbelrhiti, H., Claudin, P. & Andreotti, B. 2005 Field evidence for surface-wave-induced instability of sand dunes. Nature 437, 720–723.Google Scholar
Fernandez Luque, R. & Van Beek, R. 1976 Erosion and transport of bed-load sediment. J. Hydraul. Res. 14, 127–144.Google Scholar
Fourrière, A., Claudin, P. & Andreotti, B. 2010 Bedforms in a turbulent stream: formation of ripples by primary linear instability and of dunes by nonlinear pattern coarsening. J. Fluid Mech. 649, 287–328.Google Scholar
Frederick, K. A. & Hanratty, T. J. 1988 Velocity measurements for a turbulent nonseparated flow over solid waves. Exp. Fluids 6, 477–486.Google Scholar
Fryberger, S. G. & Dean, G. 1979 Dune forms and wind regime. A Study of Global Sand Seas 1052, 137–169.Google Scholar
Gao, X., Gadal, C., Rozier, O. & Narteau, C. 2018 Morphodynamics of barchan and dome dunes under variable wind regimes. Geology 46, 743–746.Google Scholar
Gao, X., Narteau, C. & Rozier, O. 2015a Development and steady states of transverse dunes: A numerical analysis of dune pattern coarsening and giant dunes. J. Geophys. Res. Earth Surf. 120, 2200–2219.Google Scholar
Gao, X., Narteau, C., Rozier, O. & Courrech Du Pont, S. 2015b Phase diagrams of dune shape and orientation depending on sand availability. Sci. Rep. 5, 14677.Google Scholar
Génois, M., Courrech Du Pont, S., Hersen, P. & Grégoire, G. 2013 An agent-based model of dune interactions produces the emergence of patterns in deserts. Geophys. Res. Lett. 40, 3909–3914.Google Scholar
Hardisty, J. & Whitehouse, R. J. S. 1988 Evidence for a new sand transport process from experiments on saharan dunes. Nature 332, 532–534.Google Scholar
Hersen, P. 2004 On the crescentic shape of barchan dunes. Eur. Phys. J. B 37, 507–514.Google Scholar
Hersen, P., Andersen, K. H., Elbelrhiti, H., Andreotti, B., Claudin, P. & Douady, S. 2004 Corridors of barchan dunes: stability and size selection. Phys. Rev. E 69, 011304.Google Scholar
Hersen, P., Douady, S. & Andreotti, B. 2002 Relevant length scale of barchan dunes. Phys. Rev. Lett. 89, 264301.Google Scholar
Hunter, R. E., Richmond, B. M. & Rho Alpha, T. 1983 Storm-controlled oblique dunes of the oregon coast. Bull. Geol. Soc. Am. 94, 1450–1465.Google Scholar
Iversen, J. D. & Rasmussen, K. 1999 The effect of wind speed and bed slope on sand transport. Sedimentology 46, 723–731.Google Scholar
Jackson, P. S. & Hunt, J. C. R. 1975 Turbulent wind flow over a low hill. Q. J. R. Meteorol. Soc. 101, 929–955.Google Scholar
Kouakou, K. K. & Lagrée, P.-Y. 2005 Stability of an erodible bed in various shear flows. Eur. Phys. J. B 47, 115–125.Google Scholar
Kroy, K., Fischer, S. & Obermayer, B. 2005 The shape of barchan dunes. J. Phys.: Condens. Matter 17, S1229.Google Scholar
Kroy, K., Sauermann, G. & Herrmann, H. J. 2002a Minimal model for aeolian sand dunes. Phys. Rev. E 66, 031302.Google Scholar
Kroy, K., Sauermann, G. & Herrmann, H. J. 2002b Minimal model for sand dunes. Phys. Rev. Lett. 88, 054301.Google Scholar
Lancaster, N. 1982 Linear dunes. Prog. Phys. Geog. 6, 475–504.Google Scholar
Lancaster, N. 1989 Star dunes. Prog. Phys. Geog. 13, 67–91.Google Scholar
Lancaster, N. 2013 Geomorphology of Desert Dunes. Routledge.Google Scholar
Loiseleux, T., Gondret, P., Rabaud, M. & Doppler, D. 2005 Onset of erosion and avalanche for an inclined granular bed sheared by a continuous laminar flow. Phys. Fluids 17, 103304.Google Scholar
Lü, P., Narteau, C., Dong, Z., Rozier, O. & Courrech du Pont, S. 2017 Unravelling raked linear dunes to explain the coexistence of bedforms in complex dunefields. Nat. Commun. 8, 14239.Google Scholar
Lucas, A., Narteau, C., Rodriguez, S., Rozier, O., Callot, Y., Garcia, A. & Courrech du Pont, S. 2015 Sediment flux from the morphodynamics of elongating linear dunes. Geology 43, 1027–1030.Google Scholar
Lucas, A., Rodriguez, S., Narteau, C., Charnay, B., Courrech du Pont, S., Tokano, T., Garcia, A., Thiriet, M., Hayes, A. G., Lorenz, R. D. & Aharonson, O. 2014 Growth mechanisms and dune orientation on titan. Geophys. Res. Lett. 41, 6093–6100.Google Scholar
Mainguet, M. 1984 A classification of dunes based on aeolian dynamics and the sand budget. Deserts and Arid Lands. pp. 31–58. Springer.Google Scholar
Meyer-Peter, E. & Müller, R. 1948 Formulas for bed load transport. In Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research, pp. 39–64. Inter. Assoc. for Hydraul. Res..Google Scholar
Narteau, C., Zhang, D., Rozier, O. & Claudin, P. 2009 Setting the length and time scales of a cellular automaton dune model from the analysis of superimposed bed forms. J. Geophys. Res. Earth Surf. 114, F03006.Google Scholar
Nishimori, H. & Ouchi, N. 1993 Computational models for sand ripple and sand dune formation. Intl J. Mod. Phys. B 7, 2025–2034.Google Scholar
Owen, P. R. 1964 Saltation of uniform grains in air. J. Fluid Mech. 20, 225–242.Google Scholar
Pähtz, T., Parteli, E. J. R., Kok, J. F. & Herrmann, H. J. 2014 Analytical model for flux saturation in sediment transport. Phys. Rev. E 89, 052213.Google Scholar
Parteli, E. J., Durán, O. & Herrmann, H. J. 2007 Minimal size of a barchan dune. Phys. Rev. E 75, 011301.Google Scholar
Parteli, E. J., Durán, O., Tsoar, H., Schwämmle, V. & Herrmann, H. J. 2009 Dune formation under bimodal winds. Proc. Natl Acad. Sci. USA 106, 22085–22089.Google Scholar
Parteli, E. J. R., Schwämmle, V., Herrmann, H. J., Monteiro, L. H. U. & Maia, L. P. 2006 Profile measurement and simulation of a transverse dune field in the lençóis maranhenses. Geomorphology 81, 29–42.Google Scholar
Ping, L., Narteau, C., Dong, Z., Zhang, Z. & Courrech du Pont, S. 2014 Emergence of oblique dunes in a landscape-scale experiment. Nat. Geosci. 7, 99–103.Google Scholar
Pye, K. & Tsoar, H. 1990 Aeolian Sand and Sand Dunes. Unwin Hyman.Google Scholar
Reffet, E., Courrech du Pont, S., Hersen, P. & Douady, S. 2010 Formation and stability of transverse and longitudinal sand dunes. Geology 38, 491–494.Google Scholar
Rozier, O. & Narteau, C. 2014 A real-space cellular automaton laboratory. Earth Surf. Process. Landf. 39, 98–109.Google Scholar
Rubin, D. M. & Hunter, R. E. 1987 Bedform alignment in directionally varying flows. Science 237, 276–278.Google Scholar
Rubin, D. M. & Ikeda, H. 1990 Flume experiments on the alignment of transverse, oblique, and longitudinal dunes in directionally varying flows. Sedimentology 37, 673–684.Google Scholar
Sauermann, G., Kroy, K. & Herrmann, H. J. 2001 Continuum saltation model for sand dunes. Phys. Rev. E 6403, 031305.Google Scholar
Schlichting, H., Gersten, K., Krause, E. & Oertel, H. 1955 Boundary-Layer Theory, vol. 7. Springer.Google Scholar
Schwämmle, V. & Herrmann, H. J. 2005 A model of barchan dunes including lateral shear stress. Europhys. Phys. J. E 16, 57–65.Google Scholar
Sekine, M. & Parker, G. 1992 Bed-load transport on transverse slope. I. J. Hydraul. Engng 118, 513–535.Google Scholar
Sherman, D. J. 1992 An equilibrium relationship for shear velocity and apparent roughness length in aeolian saltation. Geomorphology 5, 419–431.Google Scholar
Taniguchi, K., Endo, N. & Sekiguchi, H. 2012 The effect of periodic changes in wind direction on the deformation and morphology of isolated sand dunes based on flume experiments and field data from the western sahara. Geomorphology 179, 286–299.Google Scholar
Tuan Duc, H., Valance, A., Dupont, P. & Ould El Moctar, A. 2011 Scaling laws in aeolian sand transport. Phys. Rev. Lett. 106, 094501.Google Scholar
Ungar, J. E. & Haff, P. K. 1987 Steady state saltation in air. Sedimentology 34, 289–299.Google Scholar
Uppala, S. M., KÅllberg, P. W., Simmons, A. J., Andrae, U., Da Costa Bechtold, V., Fiorino, M., Gibson, J. K., Haseler, J., Hernandez, A., Kelly, G. A. et al. 2005 The era-40 re-analysis. Q. J. R. Meteorol. Soc. 131, 2961–3012.Google Scholar
Wasson, R. J. & Hyde, R. 1983 Factors determining desert dune type. Nature 304, 337–339.Google Scholar
Werner, B. T. 1995 Eolian dunes: computer simulations and attractor interpretation. Geology 23, 1107–1110.Google Scholar
Wilson, I. G. 1972 Aeolian bedforms-their development and origins. Sedimentology 19, 173–210.Google Scholar
Worman, S. L., Murray, A. B., Littlewood, R., Andreotti, B. & Claudin, P. 2013 Modeling emergent large-scale structures of barchan dune fields. Geology 41, 1059–1062.Google Scholar
Zhang, D., Narteau, C. & Rozier, O. 2010 Morphodynamics of barchan and transverse dunes using a cellular automaton model. J. Geophys. Res. 115, F03041.Google Scholar
Zhang, D., Narteau, C., Rozier, O. & Courrech du Pont, S. 2012 Morphology and dynamics of star dunes from numerical modelling. Nat. Geosci. 5, 463–467.Google Scholar
Zhang, D., Yang, X., Narteau, C. & Rozier, O. 2014 Mean sediment residence time in barchan dunes. J. Geophys. Res. Earth Surf. 119, 451–463.Google Scholar
Zhang, R., Kan, M. & Kawamura, T. 2005 Numerical study of the formation of transverse dunes and linear dunes. J. Phys. Soc. Japan 74, 599–604.Google Scholar
Zilker, D. P., Cook, G. W. & Hanratty, T. J. 1977 Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 1. Non-separated flows. J. Fluid Mech. 82, 29–51.Google Scholar