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Nonlinear stability and statistical mechanics of flow over topography

Published online by Cambridge University Press:  21 April 2006

George F. Carnevale  and
Jorgen S. Frederiksen
George F. Carnevale
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego. La Jolla, CA 92093, USA
Jorgen S. Frederiksen
Affiliation:
CSIRO, Division of Atmospheric Research, PB 1, Mordialloc, Victoria 3195, Australia
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Abstract

The stability properties and stationary statistics of inviscid barotropic flow over topography are examined. Minimum enstrophy states have potential vorticity proportional to the streamfunction and are nonlinearly stable; correspondingly, canonical equilibrium based on energy and enstrophy conservation predicts mean potential vorticity is proportional to the mean streamfunction. It is demonstrated that in the limit of infinite resolution the canonical mean state is statistically sharp, that is, without any eddy energy on any scale, and is identical to the nonlinearly stable minimum enstrophy state. Special attention is given to the interaction between small scales and a dynamically evolving large-scale flow. On the β-plane, these stable flows have a westward large-scale component. Possibilities for a general relation between inviscid statistical equilibrium and nonlinear stability theory are examined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 175 , February 1987 , pp. 157 - 181
Copyright
© 1987 Cambridge University Press

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