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

A finite volume method is used to study the generation, propagation and int eraction of internal waves in a linearly stratified fluid. The internal wav es were generated using single and multiple momentum sources. The full unst eady equations of motion were solved using a SIMPLE scheme on a non-stagger ed grid. An open boundary, based on the Sommerfield radiation condition, al lowed waves to propagate through the computational boundaries with minimum reflection and distortion. For the case of a single momentum source, the ef fects of viscosity and nonlinearity on the generation and propagation of in ternal waves were investigated. Internal wave-wave interactions between two wave rays were studied using tw o momentum sources. The rays generated travelled out from the sources and i ntersected in interaction regions where nonlinear interactions caused the w aves to break. When two rays had identical properties but opposite horizont al phase velocities (symmetric interaction), the interactions were not desc ribed 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 fr equencies) in the interaction region. The accumulation of the energy caused by these trapped modes within the interaction region resulted in the overt urning of the density field. When the two rays had different properties (ap art from the multiples of the forcing frequencies) the divisions of the for cing frequencies as well as the combination of the different frequencies we re observed within the interaction region. The model was validated by comparing the results with those from experiment al studies. Further, the energy balance was conserved and the dissipation o f energy was shown to be related to the degree of nonlinear interaction.