Bottom boundary layer dynamics and vorticity generation on sloping three dimensional topography

We examine sub-mesoscale dynamics in the context of steady barotropic flow past long isolated seamounts through a set of idealized regional ocean modeling system (ROMS) simulations. For an obstacle height $h_m$, width $L$ and stratification $N$, the dynamics is governed by the slope Burger number, defined as $Bu=Nh_m/fL$, where $f$ is the Coriolis parameter. The small $Bu$ limit is characterized by the development of an anticyclonic circulation on top of the seamount – a well known result in quasi-geostrophic theory. For $Bu= \mathcal{O}(1)$ and higher, reduction of bottom stress occurs both along the slope and over the top of the seamount. This stress reduction is partially due to the thermal wind shear induced by cross-slope buoyancy gradients, which opposes the ageostrophic boundary layer shear. The horizontal shear associated with boundary stress reduction leads to the generation of cyclonic vorticity on the upwelling side. Downstream development on this side is characterized by the emergence of jet-like features, intensification of cyclonic vorticity and the eventual separation and roll-up of submesoscale coherent vortices. On the downwelling side, smaller-scale centrifugal instabilities appear, coincident with patches of negative potential vorticity. Finally, in the quasi-geostrophic limit, the dynamic lift force exerted by cross-stream pressure gradients is found to be related to the barotropic circulation around the seamount, in striking analogy to the Kutta-Joukouski theorem for flow around 2D airfoils.