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This article is cited in 4 scientific papers (total in 4 papers)
Special Issue: 200th birthday of Hermann von Helmholtz
Ring Configurations of Point Vortices in Polar Atmospheres
D. G. Dritschel Mathematical Institute, University of St Andrews,
North Haugh, KY16 9SS St Andrews, UK
Abstract:
This paper examines the stability and nonlinear evolution of configurations of equalstrength
point vortices equally spaced on a ring of constant radius, with or without a central
vortex, in the three-dimensional quasi-geostrophic compressible atmosphere model. While the
ring lies at constant height, the central vortex can be at a different height and also have a
different strength to the vortices on the ring. All such configurations are relative equilibria, in
the sense that they steadily rotate about the $z$ axis. Here, the domains of stability for two or
more vortices on a ring with an additional central vortex are determined. For a compressible
atmosphere, the problem also depends on the density scale height $H$, the vertical scale over
which the background density varies by a factor $e$. Decreasing $H$ while holding other parameters
fixed generally stabilises a configuration. Nonlinear simulations of the dynamics verify the
linear analysis and reveal potentially chaotic dynamics for configurations having four or more
vortices in total. The simulations also reveal the existence of staggered ring configurations, and
oscillations between single and double ring configurations. The results are consistent with the
observations of ring configurations of polar vortices seen at both of Jupiter’s poles [1].
Keywords:
vortex dynamics, point vortices.
Received: 12.05.2021 Accepted: 15.07.2021
Citation:
D. G. Dritschel
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Abstract page: | 66 | References: | 12 |
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