Conversion of barotropic tidal energy to internal wave energy over a shelf slope for a linear stratification

The conversion of barotropic tidal energy to internal wave energy over a shelf slope is investigated using a nonlinear non-hydrostatic numerical model for several different shelf slope profiles of various amplitudes and widths and for a range of Coriolis frequencies. These idealized simulations use a linear stratification for which the buoyancy frequency is constant. Both subcritical and supercritical slopes are considered. The results are compared to two linear theories, one which is valid for small amplitude shelves while the second is valid for large amplitude shelves. Both theories are valid for subcritical slopes. We find that the small amplitude theory, which yields analytic expressions for the energy flux, overestimates the energy flux onto the shelf and underestimates the energy flux to deep water and that its accuracy deteriorates as the shelf width increases. The large amplitude theory, while more complex and requiring a numerical solution, yields results that are in good agreement with the simulations using subcritical slopes.