1202.2842 (Hygor P. M. Melo et al.)

Linear stability analysis of transverse dunes    [PDF]

Hygor P. M. Melo, Eric J. R. Partelia, José S. Andrade Jr, Hans J. Herrmann

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.

View original: http://arxiv.org/abs/1202.2842