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Advances in Mathematical Physics
Volume 2015, Article ID 613683, 9 pages
Review Article

The Ellipsoidal Vortex: A Novel Approach to Geophysical Turbulence

ISMAR-CNR, Arsenale-Tesa 104, Castello 2737/F, 30122 Venice, Italy

Received 8 October 2014; Accepted 14 January 2015

Academic Editor: Touvia Miloh

Copyright © 2015 William J. McKiver. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We review the development of the ellipsoidal vortex model within the field of geophysical fluid dynamics. This vortex model is built on the classical potential theory of ellipsoids and applies to large-scale fluid flows, such as those found in the atmosphere and oceans, where the dynamics are strongly affected by the Earth's rotation. In this large-scale limit the governing equations reduce to the quasi-geostrophic system, where all the dynamics depends on a single scalar field, the potential vorticity, which is a dynamical marker for vortices. The solution of this system is achieved by the inversion of a Poisson equation, that in the case of an ellipsoidal vortex can be solved exactly. From this ellipsoidal solution equilibria have been determined and their stability properties have been studied. Many studies have shown that this ellipsoidal vortex model, while being conceptually simple, is an extremely powerful tool in eliciting some of the fundamental characteristics of turbulent geophysical flows.