Three-dimensional sand ripples as the product of vortex instability

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Abstract

Three-dimensional sand ripples can be observed under steady liquid flows in both nature and industry. Some examples are the ripples observed on the bed of rivers and in petroleum pipelines conveying sand. Although of importance, the formation of these patterns is not completely understood. There are theoretical and experimental evidence that aquatic ripples grow from two-dimensional bed instabilities, so that a straight vortex is formed just downstream of their crests. The proposition of Raudkivi (2006), that three-dimensionality has its origin in a vortex instability, is employed here. This paper presents a linear stability analysis of the downstream vortex in order to obtain the transverse scales of three-dimensional ripples. The obtained wavelength is compared with experimentally observed ripples.

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The mechanics of dunes and antidunes in erodible-bed channels

John F. Kennedy (1963)

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Field evidence for surface-wave-induced instability of sand dunes

Hicham Elbelrhiti, Philippe Claudin, Bruno Andreotti (2005)

Field studies of barchans--crescent-shaped dunes that propagate over solid ground under conditions of unidirectional wind--have long focused on the investigation of an equilibrium between sand transport by wind and the control of air flow by dune topography, which are thought to control dune morphology and kinematics. Because of the long timescale involved, however, the underlying dynamic processes responsible for the evolution of dune fields remain poorly understood. Here we combine data from a three-year field study in the Moroccan Sahara with a model study to show that barchans are fundamentally unstable and do not necessarily behave like stable solitary waves, as suggested previously. We find that dune collisions and changes in wind direction destabilize the dunes and generate surface waves on the barchans. Because the resulting surface waves propagate at a higher speed than the dunes themselves, they can produce a series of new barchans of elementary size by breaking the horns of large dunes. The creation of these new dunes provides a mechanism for sand loss that prevents dune fields from merging into a single giant dune and therefore plays a fundamental role in the control of size selection and the development of dune patterns.