The Stability of the Bottom Boundary Layer Under a Model Mode-1 Internal Tide

The instability properties of the bottom boundary layer (BBL) under a model mode-1 internal tide in linearly stratified finite-depth water are studied, using 2D fully nonlinear and nonhydrostatic direct numerical simulations based on a spectral multidomain penalty method model. Low-mode internal tides are known to transport large amounts of energy throughout the oceans. One possible mechanism, by which the energy of the particular tidal waves can be dissipated, is through wave-BBL interactions, where near-bottom shear layers develop, leading to localized instabilities. In the model problem, the stability response of the time-dependent wave-induced BBL is examined by introducing low-amplitude perturbations near the bed. Ultimately distinct localized near-bed Kelvin Helmholtz billows are observed. The growth rate, σ, of the largest amplitude perturbation is compared to the time, T, that it is subject to a local Richardson number less than 1/4, resulting in a nondimensional criterion for instability, σT. A stability boundary is then constructed as a function of the nondimensional parameters that characterize the flow, wave steepness, aspect ratio and Reynolds number. It is shown that the nondimensional growth rate can be written as a function of these parameters, σT = F(Re,st,AR).