Dynamics and statistics of intense internal waves over a continental slope

Abstract

Nonlinear effects are essential to internal waves because of the small speed of propagation. Nonlinear internal waves are recorded by remote sensing from space and by direct measurement very often. In particular, the evolution of the semi-diurnal internal tide as it propagates across the Australian North West Shelf (NWS) leads to the formation of groups of solitons and hydraulic jumps. A numerical solution to the generalised Korteweg-de Vries (K-dV) equation, including quadratic and cubic nonlinearities, 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. The inclusion of quadratic bottom friction in the model is investigated along with the dependence on initial wave amplitude and temporal and spatial variability in the coefficients of nonlinearity and dispersion. Friction is found to be important in limiting the amplitudes of the evolving waves. The model is run using observed hydrographic conditions from the NWS. Model results are compared to current meter and thermistor observations from the shelf-break region and demonstrate good agreement with wave amplitude and waveform. Measurements of current fluctuations due to internal waves obtained on the NWS have been analysed with the aim of calculating the probability of short-scale, large-amplitude internal waves. The exceedance probability has been calculated using Poisson statistics.