Vortex crystals at Jupiter’s poles: Emergence controlled by initial small-scale turbulence

Abstract

At the poles of Jupiter, cyclonic vortices are clustered together in patterns made up of equilateral triangles called vortex crystals. Such patterns are seen in laboratory flows but never before in a planetary atmosphere, where the planet’s rotation and gravity add new physics. Siegelman (2022b) used a one-layer quasi-geostrophic (QG) model with an infinite radius of deformation to study the emergence of vortex crystals from small-scale turbulence, and Li (2020) showed that shielding of the vortices is important for the stability of the vortex crystals. Here we use the shallow water (SW) equations at the pole of a rotating planet to study the emergence and evolution of vortices starting from an initial random pattern of small-scale turbulence. The flow is in a single layer with a free surface whose slope produces the horizontal pressure gradient force. With the planet’s radius and rotation used to define the units, only three input parameters are needed to define the system: the mean kinetic energy of the initial turbulence, the horizontal scale of the initial turbulence, and the radius of deformation of the undisturbed fluid layer. We identified a non-dimensional number, $\Delta h/h$, which is related to the relative layer thickness variation of the initial turbulence and determines whether the vortex crystal or chaotic patterns emerge: Small $\Delta h/h$ values lead to vortex crystals, and large $\Delta h/h$ values lead to chaotic patterns. The value $\Delta h/h$ is related to the radius of deformation as $L_d^{-2}$. This means that a large polar radius of deformation is positively correlated to the emergence of vortex crystals, and this implies either a polar atmosphere enriched with water or deeper roots for the vortices than previously estimated.