An analytical study of general hyper-diffusivity and barotropic eddies

An exact solution to the barotropic potential vorticity equation is used to examine the properties of barotropic vortices under arbitrary nth-order hyper-diffusivity. Analytical expressions are derived for an eddy's lifetime, meridional drift, decay in size, and energy, as functions of the Coriolis parameter, order and magnitude of diffusivity, and the eddy's size, shape and strength. These expressions provide a simple explanation for many observed features of oceanic and atmospheric vortices. For example, the competition between the Coriolis effect and eddy strength in giving permitted eddy geometries; the bias towards a zonal anisotropy for large vortices but not for small ones; energetic preference for axisymmetry; poleward meridional drift of cyclonic vortices; and meridional speed variation depending on eddy geometry and strength.