Parameterizing nonhydrostatic lee wave drag with the lowest over-topping streamline

Lee waves, or internal gravity waves caused by the steady horizontal flow of stably-stratified water over bathymetry, are a ubiquitous feature in ocean currents. However, they occur on length scales that are smaller than Global Circulation Models (GCMs) can resolve. GCMs must therefore parameterize the drag on resolved currents associated with launching lee waves. This study compares the lee wave drag predicted by existing parameterizations with the drag computed using high-resolution nonhydrostatic numerical simulations of an idealized lee wave over periodic sinusoidal bathymetry. The simulations afford a time-varying glimpse at the nonlinear and nonhydrostatic oceanic lee wave spin-up process and identify a characteristic timescale to reach steady state. The maximum instantaneous lee wave drag observed during the spin-up period is found to be well predicted by linear lee wave theory for all hill heights. In steady-state, the simulations demonstrate the applicability of parameterizing the drag based on applying linear theory to the lowest over-topping streamline of the flow (LOTS), as is currently employed in GCMs. However, because existing parameterizations are based only on the height of LOTS, they implicitly assume hydrostatic flow. For hills tall enough to trap water in their valleys, the simulations identify a set of nonhydrostatic processes that can result in a reduction of the lee wave drag from that given by hydrostatic parameterizations. Together, the simulations both suggest a time-dependent nonhydrostatic version of the LOTS-based parameterization of lee wave drag and demonstrate the remarkable applicability of linear lee wave theory to oceanic lee waves.

This work is supported by ONR Grant N00014-16-1-2256.