Localized patterns of sand ripples generated by steady fows: experimental and theoretical study

Anthony Auzerais (1) , Armelle Jarno (1) , Alexander Ezersky (2) , François Marin (1)

1 LOMC - Laboratoire Ondes et Milieux Complexes
2 M2C - Morphodynamique Continentale et Côtière

In recent decades, the study of mechanisms of localized structures formation in non-equilibrium media attracted attention of researchers. Such structures were found in chemically active media, in granular materials, and in many numerical experiments with model equations. In this paper we investigate theoretically and experimentally localized patterns on sandy bottoms arising under the inuence of steady ows in the vicinity of vertical obstacle. Present experiments performed in a hydrodynamic channel show that spatially periodic quasi-stationary patterns whose width increases downstream in the wake of an obstacle arise from a sub-critical instability of the water-sandy bottom interface. We study the dependence of the topology of the area occupied by patterns on the ow velocity. It is shown that the characteristics of pattern on the bottom can be explained using the Swift-Hohenberg equation. Experiments show that for a correct description of structures, supplemented terms which take into account the impact of the vortices arising in the wake of an obstacle must be added into the Swift-Hohenberg equation.

Mots clés: steady currents; pattern formation; Swift-Ho-henberg equation; vortices; Sand ripples

Domaines: Physique [physics]

Anthony Auzerais, Armelle Jarno, Alexander Ezersky, François Marin. Localized patterns of sand ripples generated by steady fows: experimental and theoretical study. Chaotic Modeling and Simulation Journal, 2016. ⟨hal-01938695⟩