Williams, G. P., and R. J. Wilson, 1988: The stability and genesis of Rossby vortices. Journal of the Atmospheric Sciences, 45(2), 207-241.

Abstract: The stability and genesis of the vortices associated with long solitary divergent Rossby waves - the Rossby vortices - are studied numerically using the single-layer (SL) model with Jovian parameters. Vortex behavior depends on location and on balances among the translation, twisting, steepening, dispersion and advection processes. Advection is the main preserver of vortices. The solutions provide an explanation for the origin, uniqueness and longevity of the Great Red Spot (GRS).

In midlatitudes, stable anticyclones exist in a variety of sizes and balances: from the large planetary-geostrophic (PG) and medium intermediate-geostrophic (IG) vortices that propagate westward, to the small quasi-geostrophic (QG) vortices that migrate equatorward. These vortices all merge during encounters. Geostrophic vortices in the fo-plane system adjust toward symmetry by rotating; those on the sphere adjust by rotating and propagating. Stable cyclones exist mainly at the QG scale or on the fo-plane.

In low latitudes stable anticyclones exist only when a strong equatorial westerly jet and a significant easterly current are present to elininate the highly dispersive equatorial modes. The permanence of a GRS-like, low-latitude vortex in a Jovian flow configuration is established by a 100-year simulation. At the equator, stable anticyclones exist only when they have the Hermite latitudinal form and the Korteweg-DeVries longitudinal form and amplitude range as prescribed by Boyd (1980). Soliton interactions occur between equatorial vortices of similar order.

Vortices can be generated at the equator by the collapse of low-latitude anticyclones. In mid or low latitudes, unstable easterly jets generate vortices whose final number depends mainly on the interaction history. Stochastically forced eddies cascade by wave interactions into zonal currents and by eddy mergers into a single Rossby vortex that thrives on the turbulence. Directly forced ageostrophic jets can make vortex drift more westerly and can change it from free state values of -10 ms^-1 to forced state values of -5 ms^-1 (as the GRS) or of +5 ms^-1 (as the Large Ovals).