The generation of internal tides by flat-bump topography

A general procedure for the calculation of the oceanic internal tides generated by the interaction of the surface tide with bottom topography is derived, and applied to typical cases. The formalism is restricted here to essentially two-dimensional topography whose surface is never tangential to the local direction of internal tidal energy propagation, but has otherwise arbitrary shape. The theory is applicable to a wide range of density stratifications which permits a two-parameter fit to any oceanic case. Results have been calculated for certain representative topographic shapes, most notably continental slopes, and these indicate that the rate of conversion of surface tide energy into internal tide energy generally increases rapidly with topographic height, but also depends strongly on the geometry. For instance, for this model, continental slopes are far more effective internal tide generators than, say, the Mid-Atlantic Ridge. For a model ocean with constant Brunt-Väisälä frequency, N, the internal wave energy fluxes on each side of a continental slope (satisfying the above criteria) are approximately equal, but for an ocean with a realistic density profile the energy flux and energy density are larger on the shallow continental shelf than in the deep ocean.