Dynamics of counter-rotating vortex pairs in stratified and sheared environments

Abstract

The evolution of a vertically propagating vortex pair in stratified and sheared environments is studied with a two-dimensional numerical model. We consider a range of Froude (Fr) and Richardson (Ri) numbers, and a limited number of Reynolds numbers (Re). We find that stratification causes the formation of counter-sign vorticity around each of the original vortices through baroclinic production. At higher Fr, this wake vorticity advects the primary vortices closer together, decreasing their separation distance and increasing their vertical propagation speed, as predicted by Crow (1974) and Scorer & Davenport (1970). For these higher values of Fr, the wake vorticity also participates in an instability of the primary vortex pair, with the direction of propagation of the pair oscillating about the vertical. We term this instability the vortex head instability to distinguish it from the jet instabilities to which the wake itself is also susceptible. At lower Fr, internal gravity wave radiation dominates, and the intensity and spatial coherence of each vortex is rapidly reduced.When a mean horizontal flow having constant shear is present in an unstratified fluid, we find that the vortices eventually rotate about one another with the same rotational sense as the background shear flow, as predicted in Lissaman et al. (1973). When stratification is also present, we find that the distribution of baroclinically generated wake vorticity is asymmetric, which sometimes leads to the emergence of a solitary vortex with the same sign as the background shear vorticity (depending on the values of Fr, Ri, and Re). Our limited survey of parameter space indicates that a solitary vortex emerges more rapidly for smaller values of Ri, smaller values of Fr, and/or larger values of Re.