Linear stability analysis of transverse dunes |
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Authors: | Hygor PM Melo Eric JR Parteli José S Andrade Jr Hans J Herrmann |
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Institution: | 1. Departamento de Física, Universidade Federal do Ceará - 60455-760, Fortaleza, CE, Brazil;2. Institut für Baustoffe IfB, ETH Hönggerberg, HIF E 12, CH-8093, Zürich, Switzerland |
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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. |
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Keywords: | Sand dunes Pattern formation Wind erosion Granular matter Transverse instability |
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