Numerical simulation of internal tides

Abstract This work compares the numerical results of a three-dimensional hydrodynamic baroclinic model and a known analytical solution due to Baines of the baroclinic lunar semidiurnal (M2) tidal propagation over the continental shelf. The simplifying numerical approaches are the Boussinesq and the hydrostatic hypothesis. The hydrostatic pressure restricts the use of this model to every phenomenon associated with major vertical accelerations, as is sometimes the case of internal tides near steep slopes. A comparison between the two models in the area of the continental shelf was performed for 2.5, 5 and 10 per cent shelf slopes. The results obtained are the following: (a) the linear numerical solution approaches the analytical solution for these slopes, (b) the convection terms become significant for slopes greater than 5 per cent and (c) the non-linear numerical model becomes unstable for slopes above 10 per cent, therefore requiring non-hydrostatic pressure.