Numerical study of internal wave–wave interactions in a stratified fluid

Abstract

A finite volume method is used to study the generation, propagation and interaction of internal waves in a linearly stratified fluid. The internal waves were generated using single and multiple momentum sources. The full unsteady equations of motion were solved using a SIMPLE scheme on a non-staggered grid. An open boundary, based on the Sommerfield radiation condition, allowed waves to propagate through the computational boundaries with minimum reflection and distortion. For the case of a single momentum source, the effects of viscosity and nonlinearity on the generation and propagation of internal waves were investigated.

Internal wave–wave interactions between two wave rays were studied using two momentum sources. The rays generated travelled out from the sources and intersected in interaction regions where nonlinear interactions caused the waves to break. When two rays had identical properties but opposite horizontal phase velocities (symmetric interaction), the interactions were not described by a triad interaction mechanism. Instead, energy was transferred to smaller wavelengths and, a few periods later, to standing evanescent modes in multiples of the primary frequency (greater than the ambient buoyancy frequencies) in the interaction region. The accumulation of the energy caused by these trapped modes within the interaction region resulted in the overturning of the density field. When the two rays had different properties (apart from the multiples of the forcing frequencies) the divisions of the forcing frequencies as well as the combination of the different frequencies were observed within the interaction region.

The model was validated by comparing the results with those from experimental studies. Further, the energy balance was conserved and the dissipation of energy was shown to be related to the degree of nonlinear interaction.