Steady streaming and sediment transport at the bottom of sea waves

The flow and sediment transport in the boundary layer at the sea bottom due to the passage of surface waves are determined by considering small values of the wave steepness and of the ratio between the thickness of the boundary layer and the local water depth. Both the velocity field and the sediment transport rate are determined up to the second order of approximation thus evaluating both the steady streaming and the net (wave-averaged) flux of sediment induced by nonlinear effects. The flow regime is assumed to be turbulent and a two-equation turbulence model is used to close the problem. The bed load is evaluated by means of an empirical relationship as function of the bed shear stress. The suspended load is determined by computing the sediment flux, once the sediment concentration is determined by solving an appropriate advection-diffusion equation. The decay of the wave amplitude, which is due to the energy dissipation taking place in the boundary layer, is taken into account. The steady streaming and the sediment transport rate at the bottom of sea waves turn out to be different from those which are observed in a wave tunnel (U-tube), because of the dependence on the streamwise coordinate of the former flow. In particular, in the range of the parameters presently investigated, the sediment transport rate at the bottom of sea waves is found to be always onshore directed while, in a water tunnel (U-tube), the sediment transport rate can be onshore or offshore directed.