The Emergence of Multiple Robust Zonal Jets from Freely Evolving, Three-Dimensional Stratified Geostrophic Turbulence with Applications to Jupiter

Abstract

Three-dimensional numerical simulations of freely evolving stratified geostrophic turbulence on the β plane are presented as a simplified model of zonal jet formation on Jupiter. This study samples the parameter space that covers the low, middle, and high latitudes of Jupiter by varying the central latitude of the β plane. The results show that robust zonal jets can emerge from initial small-scale random turbulence through the upscale redistribution of the kinetic energy in the spectral space. The resulting flow’s sensitivities to the flow’s deformation radius LD and the two-dimensional Rhines length Lβ = (U/β)^½ (U is the characteristic turbulence velocity and β is the meridional gradient of the planetary vorticity) are tested, revealing that whether the outcome of the upscale energy transfer becomes dominated by jets or vortices depends on the relative values of LD and Lβ. The values of Lβ and LD are varied by tuning the β-plane parameters, and it is found that the flow transitions from a jet-dominated regime in Lβ ≲ LD to a vortical flow in Lβ ≳ LD. A height-to-width ratio equal to f/N, the Coriolis parameter divided by the Brunt–Väisälä frequency, has previously been established for stable vortices, and this paper shows that this aspect ratio also applies to the zonal jets that emerge in these simulations.