Turbulence-driven secondary flows and formation of sand ridges

Abstract

The mechanism of generation of sand ridges, longitudinal stripes observed both in natural rivers and in the laboratory, is investigated with the aim of showing that the initiation mechanism is intrinsically associated with an instability of the erodible bottom rather than with the effect of the secondary vortices induced by the sidewalls as suggested by previous works. A linear stability analysis of flow in infinitely wide channels with an erodible bed is then presented. In order to model the generation of turbulence-driven cellular secondary motions a nonlinear turbulence closure scheme is used. Comparison with published experimental data for the case of air duct flow over a fixed ‘ridge-shaped’ bed is performed in order to check the performance of the turbulence model and proves satisfactory. It turns out that under suitable conditions the uniform unidirectional flow is unstable with respect to spanwise disturbances with a characteristic wavelength of the order of the flow depth. This theoretical finding is supported by experimental observations on wide open-channel flows. The secondary vortices are directed in such a way as to amplify bed perturbations, eventually leading to the formation of sand ridges irrespective of the presence of the sidewalls.