To extend studies of the dynamics of thin atmospheric layers, the generation and equilibration of multiple anticyclonic vortex sets associated with long solitary baroclinic Rossby waves are examined numerically using a primitive equation model with Jovian parameters subject to a simple heating function. We seek primarily to model the three main groups of anticyclones seen on Jupiter, namely, the Great Red Spot, the three White Ovals, and the dozen or so Small Ovals that occur at latitudes of 21°, 33°, and 41°, respectively. The motions are confined to thin upper layers by exponential vertical structures that favor absolute vortex stability. Calculations are also made to examine the regeneration, intrazonal and interscale interactions, and propagation rates of vortices.Vortex sets resembling the three main Jovian groups in scale, form, and number can be simultaneously generated and maintained in a steady configuration by a heating that produces stable westerly and weakly unstable easterly jets. The steady configuration occurs when an optimal number of vortices exists in a balance between a weak heating and a weak dissipation. Vortex behavior can be more complex in the heated system because the generation of new storms offsets the tendency to merge into fewer vortices. The solutions also show that intrazonal vortex interactions can lead, in some situations, to the destruction of anticyclones modeling the Great Red Spot.