Linear stability analysis of transverse dunes

TL;DR

This paper presents a linear stability analysis demonstrating that transverse dunes are inherently unstable, with perturbations amplifying over time, explaining their decay into crescent-shaped barchans observed in experiments and simulations.

Contribution

It provides a quantitative stability analysis of transverse dunes, revealing the mechanisms behind their inherent instability and decay.

Findings

Transverse dunes are intrinsically unstable.

Perturbations grow due to lateral transport and inverse scaling of migration velocity.

Explains decay of transverse dunes into barchans in experiments and simulations.

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 along-axis perturbation on a transverse dune amplify 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 cannot exist in a stable form and decay into a chain of crescent-shaped barchans.