Lee-Vortex Formation in Free-Slip Stratified Flow over Ridges. Part I: Comparison of Weakly Nonlinear Inviscid Theory and Fully Nonlinear Viscous Simulations

Abstract

The formation of lee wakes and vortices is explored in the context of stratified flow with uniform basic-state wind and stability past elongated free-slip ridges. The theory of inviscid flow past a ridge of small nondimensional height ϵ is revisited using a weakly nonlinear semianalytic model to compute flow fields through O(ϵ2). Consistent with previous work, the weakly nonlinear solutions show an O(ϵ2) couplet of vertical vorticity above the lee slope of the appropriate sense to describe the observed circulation in lee vortices. Nonetheless, the actual O(ϵ2) flow fields are found to be inconsistent with the developing lee-vortex structures observed in previous nonlinear numerical experiments. Lee-vortex formation must therefore depend significantly on finite-amplitude and/or dissipative effects not described by the weakly nonlinear inviscid model. The weakly nonlinear results are compared to fully nonlinear numerical simulations of wake formation in viscous and thermally diffusive laminar flow. The nonlinear viscous simulations show a low-level hydraulic-jump-like structure in the lee of the obstacle, which is not predicted by the weakly nonlinear inviscid theory. A wake of decelerated fluid forms downstream of the jump with the surface flow in the wake reversing and lee vortices forming for sufficiently large ϵ. The vertical vorticity of the wake is concentrated along shear lines extending downstream from the lateral ends of the jump. In its qualitative features the low-level wake flow is surprisingly similar to previous shallow-water calculations.