Bedforms in a turbulent stream: ripples, chevrons and antidunes

International audienceThe interaction between a turbulent flow and a granular bed via sediment transport produces various bedforms associated to distinct hydrodynamical regimes. In this paper, we compare ripples (downstream propagating transverse bedforms), chevrons and bars (bedforms inclined with respect to the flow direction) and anti-dunes (upstream propagating bedforms), focusing on the mechanisms involved in the early stages of their formation. Performing the linear stability analysis of a flat bed, we study the asymptotic behaviours of the dispersion relation with respect to the physical parameters of the problem. In the subcritical regime (Froude number $\fr$ smaller than unity), we show that the same instability produces ripples or chevrons depending on the influence of the free surface. The transition from transverse to inclined bedforms is controled by the ratio of the saturation length $L_{\rm sat}$, which encodes the stabilising effect of sediment transport, to the flow depth $H$, which determines the hydrodynamical regime. These results suggest that alternate bars form in rivers during flooding events, when suspended load dominates over bed load. In the supercritical regime $\fr>1$, the transition from ripples to anti-dunes is also controlled by the ratio $L_{\rm sat}/H$. Anti-dunes appear around resonant conditions for free surface waves, a situation for which the sediment transport saturation becomes destabilising. This resonance turns out to be fundamentally different from the inviscid prediction. Their wavelength selected by linear instability mostly scales on the flow depth $H$, which is in agreement with existing experimental data. Our results also predict the emergence, at large Froude numbers, of 'anti-chevrons' or 'anti-bars', i.e. bedforms inclined with respect to the flow and propagating upstream