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The stability and energetics of corotating uniform vortices

Published online by Cambridge University Press:  20 April 2006

David G. Dritschel
David G. Dritschel
Affiliation:
Geophysical Fluid Dynamics Program, Princeton University. New Jersey 08540
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Abstract

Equilibrium shapes of two-dimensional rotating configurations of uniform vortices are numerically calculated for two to eight corotating vortices. Additionally, a perturbation series is developed which approximately describes the vortex shapes. The equilibrium configurations are subjected to a linear stability analysis. This analysis both confirms existing results regarding point vortices and shows that finite vortices may destabilize via a new form of instability derived from boundary deformations. Finally, we examine the energetics of the equilibrium configurations. We introduce a new energy quantity called ‘excess energy’, which is particularly useful in understanding the constraints on the evolution of unstable near-equilibrium configurations. This theory offers a first glance at nonlinear stability. As an example, the theory explains some features of the merger of two vortices.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 157 , August 1985 , pp. 95 - 134
Copyright
© 1985 Cambridge University Press

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