Surface Instability in Windblown Sand

TL;DR

This paper analyzes the formation and stability of windblown sand ripples using a nonlinear model, providing insights into ripple propagation, harmonic structure, and pattern stability near the onset of instability.

Contribution

It applies a nonlinear analysis to a one-dimensional sand ripple model, revealing detailed dynamics and stability boundaries of ripple patterns.

Findings

Excellent agreement between theory and simulations near instability onset

Determined ripple propagation speed and harmonic amplitudes

Identified Eckhaus boundary for pattern stability

Abstract

We investigate the formation of ripples on the surface of windblown sand based on the one-dimensional model of Nishimori and Ouchi [Phys. Rev. Lett. 71, 197 (1993)], which contains the processes of saltation and grain relaxation. We carry out a nonlinear analysis to determine the propagation speed of the restabilized ripple patterns, and the amplitudes and phases of their first, second, and third harmonics. The agreement between the theory and our numerical simulations is excellent near the onset of instability. We also determine the Eckhaus boundary, outside which the steady ripple patterns are unstable.