We examine the evolution of baroclinic vortices in a time-dependent, n
onlinear numerical model of a Jovian atmosphere. The model uses a norm
al-mode expansion in the vertical, using the barotropic and first two
baroclinic modes. Results for the stability of baroclinic vortices on
an f plane in the absence of a mean zonal flow are similar to results
of Earth vortex models, although the presence of a fluid interior on t
he Jovian planets shifts the stability boundaries to smaller length sc
ales. The presence of a barotropic mean zonal flow in the interior sta
bilizes vortices against instability and significantly modifies the fi
nite amplitude form of baroclinic instabilities. The effect of a zonal
flow on a form of barotropic instability produces periodic oscillatio
ns in the latitude and longitude of the vortex as observed at the leve
l of the cloud tops. This instability may explain some, but not all, o
bservations of longitudinal oscillations of vortices on the outer plan
ets. Oscillations in aspect ratio and orientation of stable vortices i
n a zonal shear flow are observed in this baroclinic model, as in simp
ler two-dimensional models. Such oscillations are also observed in the
atmospheres of Jupiter and Neptune. The meridional propagation and de
cay of vortices on a beta plane is inhibited by the presence of a mean
zonal flow. The direction of propagation of a vortex relative to the
mean zonal flow depends upon the sip of the meridional potential vorti
city gradient; combined with observations of vortex drift rates, this
may provide a constraint on model assumption for the flow in the deep
interior of the Jovian planets.