The generation of internal waves by flow over the rough topography of a continental slope

Abstract

Internal gravity waves generated as standing lee waves by the flow, V , of a uniformly stratified fluid over small-scale topography on an inclined slope are examined in the particular case in which the flow is parallel to the mean slope isobaths. Attention is given to the magnitude and direction of the energy flux and to its dependence on Vl / N , α and β , where l is the wavenumber of the topography, N is the buoyancy frequency of the fluid, α is the mean slope and β defines the orientation of the two-dimensional topography on the slope. In general there is a greater probability of energy transfer towards shallow water, but in particular regions the direction of the flux depends on the orientation of the topography on the slope. For a given scale of topography and for fixed longslope current, V , and stratification, N , the drag associated with the lee waves is greatest when β = 0 (when the topography is oriented normal to the mean slope isobaths) and it can be as large as the turbulent stress on the sea bed. The lee waves may induce large variations in the currents on the sea surface. It is found that although stationary lee waves may be formed over sloping topography, the waves reflected at the sea surface may subsequently be scattered from the topography to produce waves that propagate in the mean flow.