A numerical study was made on the wavelength selection mechanism of the ripples observed on the surface of a granular layer that is oscillated vertically. Multiple collisions of the one-dimensional array of beads show a time-dependent particle distribution, which induces a density wave. The magnitude of the wave velocity is estimated by the theory of elasticity, which reveals the refraction of the density wave in a quasi-two-dimensional granular layer. Our theory explains how the vertical excitation of particles determines the horizontal characteristic scale on the surface, or the wavelength of the ripples, which is applicable even to the saturation regime of a dynamically thick granular layer, e.g., the one that is thick enough to allow an immobilized region in the lower part.
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@article{CRMECA_2014__342_1_52_0,
author = {Osamu Sano},
title = {Wavelength selection of ripples in a vertically vibrating dynamically thick granular layer due to density-wave refraction},
journal = {Comptes Rendus. M\'ecanique},
pages = {52--62},
publisher = {Elsevier},
volume = {342},
number = {1},
year = {2014},
doi = {10.1016/j.crme.2013.10.006},
language = {en},
}
TY - JOUR AU - Osamu Sano TI - Wavelength selection of ripples in a vertically vibrating dynamically thick granular layer due to density-wave refraction JO - Comptes Rendus. Mécanique PY - 2014 SP - 52 EP - 62 VL - 342 IS - 1 PB - Elsevier DO - 10.1016/j.crme.2013.10.006 LA - en ID - CRMECA_2014__342_1_52_0 ER -
Osamu Sano. Wavelength selection of ripples in a vertically vibrating dynamically thick granular layer due to density-wave refraction. Comptes Rendus. Mécanique, Volume 342 (2014) no. 1, pp. 52-62. doi : 10.1016/j.crme.2013.10.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.10.006/
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☆ The paper was presented in the mini-symposium about “Recent Advances in the Mechanics of Granular and Porous Media” at the European Solid Mechanics Conference 2012 in Graz, Austria. The guest editors of this Mini-Symposium are Erich Bauer, Robert P. Behringer, Félix Darve and Lou Kondic.
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