Abstract
We explore the theory of isolated vortices in strongly sheared, deep zonal flows and the stability of these banded jets, as occur in Jupiter’s atmosphere This is done using the standard 2-layer quasigeostrophic model with the lower layer depth becoming infinite; however, this model differs from the usual layer model because the lower layer is not assumed to be motionless but has a steady configuration of alternating zonal flows. Steady state vortices are obtained by a simulated annealing computational method as generalized to fluid problems with constraints and also used in the used in the context of magnetohydrodynamics. Various cases of vortices with a constant potential vorticity anomaly atop zonal winds and the stability of the underlying winds are considered using a mix of computational and analytical techniques.
Highlights
A great red spot on Jupiter has been observed for centuries, with its present manifestation dating back to telescopic observation in 1830
We have studied the 1 34 layer model with deep sinusoidal jets and a vortex in the upper layer
The criterion for the stability of the upper layer jets, which are free to move relative to the deep flow, is that the scale of the jets must be larger than the deformation radius
Summary
A great red spot on Jupiter has been observed for centuries, with its present manifestation dating back to telescopic observation in 1830. In this paper we investigate the conditions required for isolated vortices to exist in sheared zonal flows and the stability conditions for the maintenance of zonal winds To this end we use the simple model of [3] to illustrate the basic concepts and to explore the sizes and shapes of the vortices. We review the noncanonical Hamiltonian formalism [5,6,7] and briefly describe the Dirac bracket formalism, a Hamiltonian technique for the imposition of constraints Both formalisms will be used later when we describe the simulated annealing (SA) procedure for obtaining steady states [8].
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