  We explore the conditions required for isolated vortices to exist in sheared
zonal flows and the stability of the underlying zonal winds. This is done using
the standard 2-layer quasigeostrophic model with the lower layer depth becoming
infinite; however, this model differs from the usual layer model because the
lower layer is not assumed to be motionless but has a steady configuration of
alternating zonal flows [1]. Steady state vortices are obtained by a simulated
annealing computational method introduced in [2], generalized and applied in
[3] in fluid flow, and used in the context of magnetohydrodynamics in [4-6].
Various cases of vortices with a constant potential vorticity anomaly atop
zonal winds and the stability of the underlying winds are considered using a
mix of computational and analytical techniques.
