A numerical solution to the generalized Korteweg-de Vries (KdV) equation, including horizontal variability and dissipation, is used to model the evolution of an initially sinusoidal long internal wave, representing an internal tide. The model shows the development of shocks and solitons as it propagates shorewards over the continental slope and shelf. Model results are compared to current meter and thermistor observations from the Australian North West Shelf and demonstrate good agreement with wave amplitude and waveform. It is found from observations that the coefficient of quadratic nonlinearity in the K-dV equation changes sign from negative in deep water to positive in shallow water and this plays a major role in determining the form of the internal tide transformation. On the shelf there is strong temporal variability in the nonlinear coefficient due to both background shear flow and the large amplitude of the internal tide which distorts the density profile over a wave period. Both the model and observations show the formation of an initial shock on the leading face of the internal tide. In shallow water, the change in sign of the coefficient of nonlinearity causes the shock to evolve into a tail of short period sinusoidal waves. After further propagation a second shock forms, on the back face of the wave followed by a packet of solitons. Friction is found to be important in limiting the amplitudes of the evolving waves. Modelling of the generation of the internal tide, using a primitive equation model, is briefly discussed and shows strong distortion of the internal tide from a sinusoidal form as well as the formation of bores and short period waves.
The action of the barotropic tide advecting density stratified water up and down sloping topography can result in the generation of tidal period internal waves, known as internal tides.
