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Homogenization of potential vorticity in planetary gyres

Published online by Cambridge University Press:  20 April 2006

Peter B. Rhines  and
William R. Young
Peter B. Rhines
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543
William R. Young
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543
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Abstract

The mean circulation of planetary fluids tends to develop uniform potential vorticity q in regions where closed time-mean streamlines or closed isolines of mean potential vorticity exist. This state is established in statistically steady flows by geostrophic turbulence or by wave-induced potential-vorticity flux. At the outer edge of the closed contours the expelled gradients of q are concentrated. Beyond this transition lies motionless fluid, or a different flow regime in which the planetary gradient of q may be dominant. The homogenized regions occur where direct forcing by external stress or heating within the closed isoline is negligible, upon the potential-density surface under consideration. In the stably stratified ocean such regions are found at depths greater than those of direct wind-induced stress or penetrative cooling. In ‘channel’ models of the atmosphere we again find constant q when mesoscale eddies cause the dominant potential-vorticity flux. In the real atmosphere the results here can apply only where internal heating is negligible. The derivations given here build upon the Prandtl–Batchelor theorem, which applies to non-rotating, steady two-dimensional flow. Supporting evidence is found in numerical circulation models and oceanic observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 122 , September 1982 , pp. 347 - 367
Copyright
© 1982 Cambridge University Press

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