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.
Gravity currents and internal waves in a stratified fluid
