A New Parameterization of Tidal Mixing Enhanced over Rough Seafloor Topography

It is believed that tidal interaction with rough seafloor can create mixing hotspots extending higher up off the seafloor. Although there exist parameterizations for tidal mixing enhanced over rough seafloor topography, they do not take into account the fact that the internal waves emanating from rough seafloor transit from internal tidal waves to quasi-steady internal lee waves as k_HU₀/ω increases exceeding unity where k_H is the dominant horizontal wavenumber of seafloor topography, U₀ is the amplitude of tidal flow, and ω is tidal frequency.

In this study, we formulate a new parameterization of tidal mixing enhanced over rough seafloor topography in which the vertical decay scale of energy dissipation rates is estimatedby multiplying the theoretically obtained vertical group velocities of linear internal tidal waves and quasi-steady internal lee waves, respectively, by the time scale of their nonlinear interaction (induced diffusion) with the background Garrett-Munk internal wave field. The resulting equations explicitly show that the vertical decay scale of energy dissipation rates becomes (1) independent of U₀ but inversely proportional to k_H squared for k_HU₀/ω < 1 and (2) independent of k_H but proportional to U₀ squared for k_HU₀/ω > 1, which explain very well the features obtained from eikonal calculations for quasi-steady internal lee waves and numerical experiments for linear internal tidal waves, respectively, emanating from the seafloor.

It is confirmed that thus formulated parameterization predicts the vertical distribution ofenergy dissipation rates in agreement with that obtained from eikonal calculations for linear internal tidal waves and quasi-steady internal lee waves emanating from rough seafloor.