Improving Nonlinear and Nonhydrostatic Ocean Lee Wave Drag Parameterizations

Ocean lee waves occur on length scales that are smaller than the grid scale of global circulation models (GCMs). Therefore, such models must parameterize the drag associated with launching lee waves. This paper compares the lee wave drag predicted by existing parameterizations with the drag measured in high-resolution nonhydrostatic numerical simulations of a lee wave over periodic sinusoidal bathymetry. The simulations afford a time-varying glimpse at the nonlinear and nonhydrostatic oceanic lee wave spinup process and identify a characteristic time scale to reach steady state. The maximum instantaneous lee wave drag observed during the spinup 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 overtopping streamline of the flow (LOTS), as is currently employed in GCMs. However, because existing parameterizations are based only on the height of the 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. The simulations suggest implementing 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.