Linear stability analysis of transverse dunes
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 391 (20):
4606-4614 (2012)DOI: 10.1016/j.physa.2012.05.042
Abstract
Sand-moving winds blowing from a constant direction in an area of high
sand availability form transverse dunes, which have a fixed profile in
the direction orthogonal to the wind. Here we show, by means of a linear
stability analysis, that transverse dunes are intrinsically unstable.
Any perturbation in the cross-wind profile of a transverse dune
amplifies in the course of dune migration due to the combined effect of
two main factors, namely: the lateral transport through avalanches along
the dune's slip-face, and the scaling of dune migration velocity with
the inverse of the dune height. Our calculations provide a quantitative
explanation for recent observations from experiments and numerical
simulations, which showed that transverse dunes moving on the bedrock
(or ``transverse sand ridges'') cannot exist in a stable form and
decay into a chain of crescent-shaped barchans. (C) 2012 Elsevier B.V.
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