Vorticity and potential vorticity in mountain wakes

A wake is traditionally defined as the region of nearly stagnant how downst ream of a body in a uniform stream. In a stratified fluid, the motions and density surfaces downstream of an obstacle become primarily horizontal; the vertical component of the vorticity associated with the wake, coexisting w ith the stable vertical density stratification, implies that there is poten tial vorticity (PV) in the wake. Recent work has demonstrated that dissipat ion aloft, associated with a breaking mountain wave over an isolated peak, produces a dipole in PV downstream; the dipolar vertical vorticity of the w ake is associated with the PV dipole. Although one may infer the existence of vorticity downstream, the PV argument is silent on the question, Where d oes the wake vorticity come from? To answer this question, a weakly nonline ar model for PV production and wake formation in the case of a small-amplit ude mountain has been analyzed, and numerical simulations pertaining to the strongly nonlinear large-amplitude case have been carried out. The simple model indicates that even with dissipation in the system, the vertical vort icity of the wake arises through the tilting of baroclinically generated ho rizontal vorticity by the dissipating mountain wave. This analysis shows th at there need not be any direct effect of friction in the vorticity equatio n to produce the vorticity of the wake; dissipation (due to friction and/or heating) enters indirectly through its effect on the tilting term. Analysi s of numerical simulations of the large-amplitude case shows that the concl usions from the weakly nonlinear model regarding the source of wake vortici ty continue to hold in the strongly nonlinear regime.