A New Parameterization of Turbulent Mixing Enhanced Over Rough Seafloor Topography

Existing parameterizations of turbulent mixing enhanced over high-wavenumber seafloor topography miss the fact that internal tidal waves emanating from the seafloor transform to internal lee waves as the tide-topography interaction strengthens. This motivates us to replace the vertical decay scale of bottom-enhanced turbulent mixing with the "vertical mean free path" of internal lee waves, namely, the average vertical distance over which internal lee waves propagate until they discharge their energy through interactions with the background internal waves. The resulting formula shows that the vertical extent of turbulent mixing becomes proportional to the abyssal barotropic tidal or steady flow amplitude squared and the inverse abyssal buoyancy frequency squared, but independent of the wavenumber of the seafloor, consistent with recent eikonal calculations and field observations. We propose a new parameterization of turbulent mixing enhanced over high-wavenumber seafloor topography through incorporating the formulated vertical decay scale.