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Pseudo-advective relaxation to stable states of inviscid two-dimensional fluids

Published online by Cambridge University Press:  26 April 2006

G. F. Carnevale  and
G. K. Vallis
G. F. Carnevale
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA
G. K. Vallis
Affiliation:
Division of Natural Sciences, University of California, Santa Cruz, Santa Cruz, CA 95064, USA
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Abstract

The continuous transformation of one flow into another of higher or lower energy while preserving the potential vorticity of all particles can be accomplished by advection with an artificial velocity field. Since isolated extremal energy states are stable states, this method can be used to find stable stationary flows on a prescribed isovortical sheet. A series of numerical simulations of this method for two-dimensional fluids that demonstrates its feasibility and utility is presented. Additionally, a corollary to Arnol'd's nonlinear stability theorems is discussed, which shows that there can be at most two Arnol'd stable states per isovortical sheet.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 213 , April 1990 , pp. 549 - 571
Copyright
© 1990 Cambridge University Press

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