Shocks in the internal tide on the Australian North West Shelf

The evolution of shocks in the semi-diurnal internal tide on the Australian North West Shelf has previously been studied and an analytic solution has been found in terms of non-physical variables. Conversion of the results to physical variables requires the solution of the modal equation which can be solved analytically only if the background velocity profile is linear or constant. In this study the modal equation is solved numerically and this solution is used to study the effect of nonlinear background velocity profiles. It is found that profiles which are compatible with the profile of averaged currents can explain the observed shock heights as long as there is a strong shear near the surface.