A nearly ubiquitous feature of planetary atmospheres in the solar system are rapidly rotating flows in polar regions, that are generally referred to as polar vortices. These features may be explained by consideration of basic physical constraints. At the most fundamental level, rapidly rotating planets have a minimum of angular momentum on the axis of rotation, and a maximum at the equator. Due to their rotation, planetary bodies may be expected to develop polar cyclonic flow as a result of transport of air between different latitudes, which will tend to increase the angular momentum at high latitudes, and decrease it at low latitudes. Such transport may arise through a variety of forms, including turbulence and wave stresses or the induced circulation arising from local heating or cooling anomalies (Andrews et al., 1987).Transport of angular momentum alone, however, cannot be used directly to determine the development of cyclonic polar motions because background rotation and density stratification combine to place further dynamical constraints on the nature of the transport. An elegant way to view these constraints is through another dynamical quantity, the potential vorticity (PV), closely related to angular momentum and its conservation. PV, q, may be defined as,