Vortex formation and vortex shedding in continuously stratified flows past isolated topography

The flow of a nonrotating atmosphere with uniform stratification and wind speed past an isolated three-dimensional topographic obstacle is investigated with a nonhydrostatic numerical model having a free-slip lower boundary. When the mountain is sufficiently high, the transient development of a quasi-steady flow occurs in two phases. During the first phase, which occurs over a dimensionless time of O(1), the flow is essentially inviscid and adiabatic, and potential vorticity (PV) is conserved. The transient evolution of the flow during the second phase, which occurs over a dimensionless time of O(10) to O(100), is controlled by dissipation and is accompanied by the generation of PV anomalies. Two cases are examined in which the flow is forced to remain left-right symmetric with respect to the axis of the incident flow. In the first, the dimensionless mountain height NH/U is 1.5, and gravity waves break over the mountain. In the second, NH/U = 3, and a quasi-steady recirculating wake containing a doublet of positive and negative vortices develops in the lee. In both cases potential vorticity anomalies are generated by dissipation, although the sources of dissipation are different in each case. The net effect of the dissipation on the PV budget is, nevertheless, similar as may be understood from the generalized Bernoulli theorem that equates the generation of potential vorticity fluxes to the development of a Bernoulli function gradient on quasi-steady isentropic surfaces. In these experiments a Bernoulli deficit develops either from strong localized dissipation in the wave-breaking region (dominant for NH/U = 1.5), or as the result of weak dissipation throughout the elongated wake (dominant for NH/U = 3). Oscillating von Karman vortex streets appear if the flows are allowed to develop asymmetries with respect to the axis of the incident flow. It is shown that the transition into the vortex shedding regime is associated with an absolute instability of the symmetrical wake, which feeds upon the shear present at the edges of the wake. The most unstable global normal mode is diagnosed numerically and shows strong similarities with the corresponding mode in shallow-water theory. The doubling time of the instability is a few hours, which is consistent with the rapid formation of observed atmospheric vortex streets. The individual vortices in the fully developed vortex street are quasi-balanced warm-core vortices that are associated with both PV and surface potent