This study of nonlinear processes and turbulence associated with internal gravity waves has three phases. In the first phase, the reflection problem is studied with simulations involving laboratory-scale slopes whose inclination varies between critical (resonant case with slope angle equal to wave propagation angle) and somewhat off-critical values. We start with three-dimensional direct numerical simulation (DNS) and find strong nonlinearity in the response if the off-criticality is not too large: harmonics in the radiated wave field and cyclical near-bottom turbulence. Subharmonic frequencies are found slightly away from the interaction region in some cases, prompting a followup study with two-dimensional simulations where the underlying mechanism is identified as parametric subharmonic instability (PSI) of the reflected wave beam: the sum of the frequencies and the sum of the wave numbers of the daughter subharmonic waves equal the corresponding quantities for the reflected wave. This is the first demonstration that the reflected wave formed when a small-amplitude linear wave is incident on a slope becomes sufficiently nonlinear so as to suffer PSI.
In the second phase, DNS and large eddy simulation (LES) are employed to study the turbulent dissipation and mixing brought about by convective overturns in a stratified, oscillatory bottom layer underneath internal waves. The phasing of turbulence, the onset and breakdown of convective overturns, and the pathway to irreversible mixing are quantified. $L_T$ decreases during the convective instability while $L_O$ increases, which implies that $L_T$ is not linearly related to $L_O$. Thus, the instantaneous Thorpe-inferred dissipation rates are quite different from the actual values. However, the ratio of their cycle-averaged values is found to be O(1).
In the third phase, a novel modeling technique called SOMAR-LES has been developed wherein a three-dimensional, body-conforming Large Eddy Simulation (LES) model that resolves turbulence scales is coupled with the large-sale Stratified Ocean Model with Adaptive Refinement (SOMAR) to accurately represent small scale turbulence as well as its effect on flow evolution at large scale. Numerical simulations are performed with coupled SOMAR-LES to examine the flow at model Kaena ridge, a steep supercritical generation site.
