β-Plane Corrections to Nonlinear Atmospheric Flow Patterns: Application to Jupiter’s Great Red Spot (GRS) Drift Dynamics

The Great Red Spot (GRS) of Jupiter has been observed for over a century, with researchers studying itscharacteristics and dynamics, including its size, depth, movement, and interactions with its environment.Recently, the f -plane thin-shell asymptotic analysis was used to explain some of the GRS features, butthe method failed to capture the observed westward drift of the GRS. In this study, the f-plane theory wasextended by including the Rossby parameter in the β-plane approximation and using the dimensionless Rossbydeformation parameter γ, to systematically apply perturbation theory. The westward drift velocity of 3.7m/s was analytically predicted, which is 95% in agreement with the observed 3.9 m/s. The observed 90-dayoscillation in drift rate was explained. Also explained is the north-south asymmetry in circulation patterns.The universality of the β-plane theory was demonstrated by its application to the vortices on Saturn, Neptuneand Earth, without free parameters. It was demonstrated in this study that for the understanding of long-livedatmospheric vortex dynamics, the planetary vorticity gradient is very critical.