The impacts of ocean bottom roughness and tidal flow amplitude on abyssal mixing

Existing parameterizations of vertical mixing over a rough ocean bottom neglect the transformation of linear internal waves into quasi-steady internal lee waves, which occurs when tide-topography interactions strengthen. In the present study, we perform a series of eikonal calculations to investigate the energy transfers from upward propagating quasi-steady internal lee waves to dissipation scales through nonlinear interactions with the background Garrett-Munk internal waves. For a fixed density stratification, the vertical group velocity of the quasi-steady internal lee wave increases as either the horizontal wave number of the bottom topography or the tidal flow amplitude increases, whereas the life time of the quasi-steady internal lee wave decreases as the horizontal wave number of the bottom topography increases but is relatively independent of the tidal flow amplitude. Consequently, the resulting bottom-enhanced vertical mixing extends further upward as the tidal flow amplitude increases, nearly independent of the bottom roughness. We also find a tradeoff between the fraction of energy dissipated at the ocean bottom and the vertical extent of the energy dissipation region above the ocean bottom.