Lee vortex formation in stratified flow over 3d ridges

The formation of lee wakes and vortices in stratified flow over three-dimensional ridges is studied in the absence of surface friction and planetary rotation. Comparison of weakly nonlinear semi-analytic calculations and fully nonlinear numerical simulations reveals the importance of a fully nonlinear stratified analog to a hydraulic jump downstream of the obstacle. The dynamics leading to vortex formation in the nonlinear simulations is clarified through an analysis based on a Lagrangian decomposition of the vorticity according to source. The low-level lee-slope flow leading into the jump along the interior of the ridge is found to have relatively weak vertical shear due to the free-slip condition at the lower boundary. Upon crossing the jump the flow deepens, decelerates, and gaines positive vertical shear due to the buoyancy gradient across the jump. The conditions downstream of the jump are then consistent with reversal of the surface flow. In plan view it is found that weak vertical vorticity originating in the mountain wave upstream of the jump is strongly amplified by vertical stretching in the jump to produce the pronounced vertical vorticity anomalies at the lateral edges of the wake.