Parameterizing Nonpropagating Form Drag over Rough Bathymetry

Slowly evolving stratified flow over rough topography is subject to substantial drag due to internal motions, but often numerical simulations are carried out at resolutions where this wave'' drag must be parameterized. Here we highlight the importance of internal drag from topography with scales that cannot radiate internal waves, but may be highly nonlinear, and we propose a simple parameterization of this drag that has a minimum of fit parameters compared to existing schemes. The parameterization smoothly transitions from a quadratic drag law (similar to hu(0)(2)) for low Nh/u(0) (linear wave dynamics) to a linear drag law (similar to h(2)u(0)N) for high Nh/u(0) flows (nonlinear blocking and hydraulic dynamics), whereNis the stratification, h is the height of the topography, and u(0) is the near-bottom velocity; the parameterization does not have a dependence on Coriolis frequency. Simulations carried out in a channel with synthetic bathymetry and steady body forcing indicate that this parameterization accurately predicts drag across a broad range of forcing parameters when the effect of reduced nearbottom mixing is taken into account by reducing the effective height of the topography. The parameterization is also tested in simulations of wind-driven channel flows that generate mesoscale eddy fields, a setup where the downstream transport is sensitive to the bottom drag parameterization and its effect on the eddies. In these simulations, the parameterization replicates the effect of rough bathymetry on the eddies. If extrapolated globally, the subinertial topographic scales can account for 2.7TW of work done on the low-frequency circulation, an important sink that is redistributed to mixing in the open ocean.

Automated summary

The study emphasizes the importance of internal drag from topography and proposes a simple parameterization scheme. Simulations show that the parameterization accurately predicts drag under different forcing parameters and replicates the effect of rough bathymetry on eddies in wind-driven channel flows.