Bedforms in a turbulent stream: ripples, chevrons and antidunes

The interaction between a turbulent flow and a granular bed via sediment transport produces various bedforms associated with 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 antidunes (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 F 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 controlled by the ratio of the saturation length L-sat, which encodes the stabilizing 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 bedload. In the supercritical regime F > I, the transition from ripples to antidunes is also controlled by the ratio L-sat/H. Antidunes appear around resonant conditions for free surface waves, a situation for which the sediment transport saturation becomes destabilizing. 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 'antichevrons' or 'antibars', i.e. bedforms inclined with respect to the flow and propagating upstream.