A Nonlinear Model of Internal Tide Transformation on the Australian North West Shelf

Abstract

A numerical solution to the generalized Korteweg-de Vries (K-dV) 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 the waveform to the formation of shocks and solitons as it propagates shoreward over the continental slope and shelf. The model is run using observed hydrographic conditions from the Australian North West Shelf and results are compared to current meter and thermistor observations from the shelf-break region. It is found from observations that the coefficient of 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. The inclusion of bottom friction in the model is investigated along with the dependance on initial wave amplitude and variability in the coefficients of nonlinearity and dispersion. Friction is found to be important in limiting the amplitudes of the evolving waves.