Simulating Jupiter’s Great Red Spot with Discrete Exterior Calculus

Abstract

The giant vortex in Jupiter's atmosphere, the great red spot (GRS), has grabbed attention of not only astrophysicists but also of fluid dynamists. What fluid dynamics/thermodynamics conditions might have formed it and made it extremely stable and long-lived are some fundamental questions of interest, and the present work addresses these. We model the GRS numerically using a structure-preserving Discrete Exterior Calculus (DEC) method. Our initial condition comprises of vortices embedded in a shearing zonal flow. We solve the continuity and momentum equation (that conserves the potential vorticity) on a sphere (thereby including sphericity and excluding domain boundary influence), for incompressible, inviscid flow with uniform fluid properties. We investigate the vorticity dynamics of vortices in shearing zonal flows for a range of parameters. Our simulations show evolution of a stable vortex in a zonal band similar to the GRS.

A primitive variable discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

“…24 DEC has low numerical diffusion and superior conservation of physical quantities such as vorticity and kinetic energy and preserves vortical structures over a long period of time. 21,27 We conjecture that these properties potentially make DEC favorable for turbulence simulations in three dimensions.…”