Steady streaming induced by sea waves over rippled and rough beds

The flow in the boundary layer generated close to the sea bottom by the propagation of a monochromatic surface wave is determined by considering small values of both the wave steepness and the ratio between the thickness of the boundary layer and the local water depth. Nonlinear effects are considered and attention is focussed on the steady streaming. The sea bed is assumed to be horizontal, impermeable and rippled and the small scale bedforms are supposed to act as a large roughness the size of which depends on the ripple height. The analysis of Blondeaux et al. (2012), who considered a flat bed, is thus extended. The geometrical characteristics of the ripples are predicted using empirical formulae and, then, the bedforms are assumed to behave as a bottom roughness, the size of which is related to the size of the ripples. A comparison of the model results with experimental measurements supports the theoretical findings. As in the sheet flow regime (when the sea bed is flat), the steady streaming at the bottom of sea waves is found to be different from that predicted in an oscillating water tunnel (U-tube). Moreover, it is found that ripples interacting with a propagating wave can generate a steady streaming which points either in the onshore direction or in the offshore direction, depending on the value of the physical parameters.