Abstract.
From a phenomenological hydrodynamical model, we analyze the aeolian sand ripple evolution in an out-of-equilibrium aeolian regime where erosion exceeds accretion (and vice versa). We find, in particular, that the ripple structure can be destroyed in favor of a flat sand bed. In the ripple regime we report on a new class of generic dynamics described by the Benney equation. This equation reveals either order or disorder depending on whether wave dispersion is strong or weak. In both cases, the average wavelength of the pattern is fixed in time. This markedly contrasts with the regime of equilibrium aeolian regime -reached when erosion balances deposition- where ripples undergo a coarsening process at long time (i.e., the wavelength increases indefinitely with time).
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References
R.A. Bagnold, The Physics of blown sand and desert dunes (Chapmann and Hall, Methuen, London, 1941)
D. Bideau, A. Hansen, Disorder and Granular media (North-Holland, Amsterdam, 1993)
R. Anderson, Sedimentology 34, 943 (1987)
R. Hoyle, A. Woods, Phys. Rev. E 56, 6861 (1997)
R. Anderson, Earth-Sci Rev. 29, 77 (1990)
H. Nishimori, N. Ouchi, Int. J. Mod. Phys. B 7, 2025 (1993)
H. Nishimori, N. Ouchi, Phys. Rev. Lett. 71, 197 (1993)
W. Landry, B. Werner, Physica D 77, 238 (1994)
R. Anderson, K. Bunas, Nature 365, 740 (1993)
O. Terzidis, P. Claudin, J.-P. Bouchaud, Eur. Phys. J. B 5, 245 (1998)
F. Rioual, A. Valance Eur. Phys. J. B 10, 543 (1999)
Z. Csahok, C. Misbah, F. Rioual, A. Valance, Eur. Phys. J. E 3, 71 (2000)
Z. Csahok, C. Misbah, A. Valance, Physica D 28, 87 (1999)
J.-P. Bouchaud, M. Cates, J.R. Prakash, S.F. Edwards, J. Phys. France I 4, 1382 (1994)
F. Rioual, A. Valance, D. Bideau, Phys. Rev. E 62, 2450 (2000)
F. Rioual, Ph.D. Dissertation, University of Rennes (2002)
G. Sauermann, K. Kroy, H. Herrmann, Phys. Rev. E 64, 31305 (2001)
D. Benney, J. Math. Phys. 45, 150 (1966)
M. Sato, M. Uwaha, Europhys. Lett. 32, 639 (1995)
C. Misbah, O. Pierre-Louis, Phys. Rev. E 53, R4318 (1996)
B. Janiaud, A. Pumir, D. Bensimon, V. Croquette, H. Richter, L. Kramer, Physica D 55, 77 (1992)
D. Douglas, D. Hong, Phys. Rev. E 52, 218 (1995)
Y. Kuramoto, T. Tsuzuki, Prog. Theor. Phys. 55, 356 (1976); G. Sivashinsky, Acta Astronautica 4, 1177 (1977)
F. Gillet, C. Misbah, unpublished
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Received: 4 August 2003, Published online: 5 February 2004
PACS:
81.05.Rm Porous materials; granular materials
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Misbah, C., Valance, A. Sand ripple dynamics in the case of out-of-equilibrium aeolian regimes. Eur. Phys. J. E 12, 523–529 (2003). https://doi.org/10.1140/epje/e2004-00024-5
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DOI: https://doi.org/10.1140/epje/e2004-00024-5