Resonant triad model for studying evolution of the energy spectrum among a large number of internal waves

Abstract

Internal waves are generally accepted to be responsible for a large fraction of mixing in the deep ocean. Internal waves interact nonlinearly with one another, exchanging energy among themselves to create the background internal wave spectrum. The most important mechanism resulting in the transfer of energy from one wave to another is believed to be resonant triad interactions. In this paper we consider a large number of resonantly interacting triads in order to investigate the evolution of the energy spectrum due to solely resonant triad interactions. To this end we solve the evolution equations for a large number of resonant triads to determine the temporal evolution of the energy distribution among the various possible wave numbers and frequencies. Our model involves internal waves with frequencies spanning the range of possible frequencies, i.e., between a maximum of the buoyancy frequency N for horizontal wave vectors (vertical motion) to a minimum of the inertial frequency f for vertical wave vectors (horizontal motion) [two limiting cases]. Because of the inclusion of high-frequency waves we cannot make the hydrostatic approximation. We investigate the evolution of the wave’s amplitudes to predict the evolution of the internal wave energy spectrum.