Numerical simulations of the interaction of internal waves with a shelf break

Abstract

The energetics of the interaction of internal gravity waves with a shelf break is investigated by means of high-resolution two-dimensional numerical simulations, with an emphasis on understanding the partitioning of the internal wave energy over the course of the interaction process and the subsequent dynamics of the onshore propagating internal waves. Some of the energy is dissipated as a result of the instabilities associated with breaking, while the remaining energy is either reflected back away from or transmitted onto the shelf. We employ an analysis of the distribution of the energy flux across the shelf break taking into account the contributions from nonhydrostatic as well as nonlinear effects to quantify the percentage of energy flux that is transmitted onto the shelf, as well as the percentages of reflected and dissipated energy fluxes, from an incoming wave field. For a given frequency of an incoming wave, we vary the amplitude of the wave to vary the incident energy flux, and we simulate conditions ranging from subcritical to supercritical slopes by varying the topographic slope angle. The results show that the cumulative transmitted energy flux is a strong function of the ratio of the topographic slope γ, to wave characteristic slope s, while the reflected energy flux is a strong function of both γ∕s as well as the nonlinearity. The energy flux calculations indicate that the internal boluses that form as a result of the interaction of the incident wave with the slope are very energetic, especially for critical to supercritical slopes. These nonlinear internal waves are plausible candidates for effectively transporting mass onshore, not withstanding their contribution to diapycnal mixing as well.