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.