Eddy-jet interaction theorems for piecewise constant potential vorticity flows
George I. Bell
and Larry J. Pratt
Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
Received 15 July 1991; revised 29 May 1992; accepted 30 June 1993. ; Available online 8 April 2003.
Abstract
Integral constraints governing interactions between jets and detached eddies are discussed for quasigeostrophic flows with piecewise uniform potential vorticity. Building on the work of Dritschel (Journal of Fluid Mechanics, 191: 575–581 (1988b)), we use conservation of pseudomomentum to predict the propagation direction of eddies (closed fronts) or place bounds on their excursions. The piecewise uniform condition also allows for a simple interpretation of a well-known eddy-mean flow interaction theorem. Specifically, it is shown that mean zonal velocity is equal to its undisturbed value plus a weighted sum of displaced areas (or volumes) under fronts which have crossed the latitude line in question. All results are valid regardless of the amplitude or shape of frontal disturbances.
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