An Idealized 3D Model of Interfacial Instability of Aeolian Bedform

Abstract

An idealized morphodynamic model is constructed for formation of the aeolian sand ripples from small bottom perturbations of a two-dimensional sand bed. The main goal of the analysis is to evaluate the influence of the gravity flow (including “impact-induced gravity flow” in the reptation flux and “topography-induced gravity flow” in the creep flux) on the formation of the aeolian sand ripples and to clarify the relative contribution of various factors to the bed instability. A 3D linear stability analysis reveals that gravity flow appreciably affects the dynamics behaviors of aeolian sand ripples, which decreases the growth rate of sand ripples, tends to stabilize the sand bed, and leads to longer wavelength. We found that the competition between the destabilizing effect of reptation flow and the stabilizing effects of gravity flow leads to pattern selection. The along-crest diffusion of topography driven by impact and gravity is beneficial to the transverse stability of sand ripples, producing sand ripples with straighter and more continuous crests. For moderate values of D, the most unstable mode has zero value of the transverse wavenumber (ky = 0), thus corresponding to aeolian ripples with crests perpendicular to the wind. Moreover, when the impact angle is 9–16°, it has little effect on the characteristics of sand ripples for the initial stage of ripple development. For every increase of the impact angle by 1°, the initial wavelength only increases by about 1.5%. In conclusion, the influence of the gravity flow on the dynamics of sand ripples formation stage cannot be neglected.