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 f0-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 f0-plane. In low latitudes ...