Refraction and shoaling of nonlinear internal waves at the Malin shelf break

This paper applies a numerical model to explain the refraction and shoaling of nonlinear internal waves observed at the Malin slope for a sequence of tidal cycles in the summer of 1995. The model is first order in dispersion and second order in nonlinearity and is based on the extended Korteweg - de Vries (EKdV) equation. The EKdV model is applied along a set of rays and includes the effect of variable depth. The model predicts that an initial long-wavelength wave, which lies in water of depths between 500 and 900 m, develops into a set of internal solitary waves as it passes across the shelf break and onto the continental shelf, in agreement with observations. The extent of refraction is small because the internal waves are high frequency, and in this case the refraction is not strongly dependent on the nonlinear adjustment to phase speed. In the observations, the internal-wave amplitude, measured in terms of near-surface currents or thermocline displacement, initially grows as the wave crosses the slope and then is capped as the shelf is reached. The numerical experiments suggest that this behavior is due to a particular nonlinear feature of the EKdV equation, which predicts the existence of limiting wave amplitudes. The properties of simulated internal waves that arose from an idealized initial waveform were close to those observed. However, the numerical evolution of waves from a realistic initial condition showed some differences to the observed. It is suggested that these differences are due to neglect of strong nonlinearity and turbulence in the model.