DOI: 10.1007/s101890070043
Dynamics of aeolian sand ripples
Z. Csahók1, 2, C. Misbah1, F. Rioual3 and A. Valance31 Laboratoire de Spectrométrie Physique, Université Joseph Fourier (CNRS), Grenoble I, B.P. 87, Saint-Martin d'Hères, 38402 Cedex, France
2 MTA Research Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary
3 Groupe Matière Condensée et Matériaux, UMR 6626, Université Rennes 1, 35042 Rennes Cedex, France
alexandre.valance@univ-rennes1.fr
(Received 20 January 2000)
Abstract
We analyze theoretically the dynamics of aeolian sand ripples. In order
to put the study in the context, we first review existing models.
This paper is a continuation of two
previous papers (Z. Csahók et al., Physica D 128, 87 (1999);
A. Valance et al., Eur. Phys. J. B 10, 543 (1999)), the first
one is based on symmetries and the second
on a hydrodynamical model.
We show how the hydrodynamical
model may be modified to recover the missing terms
that are dictated by symmetries.
The symmetry and conservation arguments are powerful in that
the form of the equation is model-independent.
We then present
an extensive numerical and analytical
analysis of the generic sand ripple equation. We find
that at the initial stage the wavelength of the ripple is that
corresponding to the linearly most dangerous mode. At later
stages the profile undergoes a coarsening process leading
to a significant increase of the wavelength. We find
that including the next higher-order nonlinear term
in the equation leads naturally to a saturation of the local slope.
We analyze both
analytically and numerically the coarsening stage, in terms of
a dynamical exponent for the mean wavelength increase. We discuss
some future lines of investigations.
83.70.Fn - Granular solids.
81.05.Rm - Porous materials; granular materials.
47.20.-k - Hydrodynamic stability.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2000
