Lee-Vortex Formation in Free-Slip Stratified Flow over Ridges. Part II: Mechanisms of Vorticity and PV Production in Nonlinear Viscous Wakes

The formation of orographic wakes and vortices is studied within the context of numerically simulated viscous flow with uniform basic-state wind and stability past elongated free-slip ridges. The viscosity and thermal diffusivity are sufficiently large that the onset of small-scale turbulence is suppressed. It is found in Part I of this study that wake formation in the viscous flow is closely tied to the dynamics of a low-level hydraulic-jumplike feature in the lee of the obstacle. Here the role of the hydraulic jump in producing the vorticity and potential vorticity (PV) of the viscous wake is considered. A method for diagnosing vorticity production is developed based on a propagator analysis of the Lagrangian vorticity equation that generalizes Cauchy’s formula for the evolution of vorticity in a Lagrangian framework. Application of the method reveals that the vertical vorticity of the wake originates through baroclinic generation and tilting in the mountain wave upstream of the jump. However, upstream of the jump the vertical vorticity is relatively weak. Vertical stretching in the jump then amplifies this vorticity significantly to produce the pronounced vertical vorticity anomalies along the shear lines at the lateral edges of the wake. The PV of the wake is found to result mainly from thermal dissipation in the jump. In particular, thermal diffusion tends to diabatically modify the potential temperature field in the jump so as to create PV from the vertical vorticity already present. From the standpoint of PV conservation, the presence of both diabatic cooling (by thermal diffusion) and vertical vorticity at the base of the jump produces a vertical flux of PV through the lower boundary. The advective fluxes of PV along each side of the wake are then primarily balanced at steady state by fluxes of PV through the obstacle surface.