Energy-enstrophy balance and the evolving shape of Jupiter’s Great Red Spot

Inspired by the statistical mechanics approach to the organization of two-dimensional turbulence into a steady flow, we propose a variational principle to explain the observed tendency of Jupiter’s Great Red Spot (GRS) to become more circular. For this, we first derive, at leading order in the thin-shell parameter, a consistent set of nonlinear governing equations for the leading-order dynamics of flows confined to a thin zonal band in Jupiter’s upper troposphere, near the cloud tops. Jupiter’s internal heat source and interactions with the ambient flow may modify the kinetic energy of the GRS but its enstrophy is conserved at leading order. Within the framework of the leading-order dynamics, we show that the state of maximal kinetic energy at a fixed enstrophy for a prescribed area corresponds to a circular vortex and that this energetically optimal state is nonlinearly stable. This provides an energetic benchmark for interpreting the observed rounding trend of the GRS, with velocity and thermal features of the optimizer consistent with recent data. However, the discrepancy between the optimizer’s center-peaked vorticity profile and the observed hollow core shows that the optimizer is not an inevitable terminal state. Interactions with the ambient flow, radiative losses and three-dimensional stratified dynamics are factors that may prevent the GRS from attaining it.