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A geometric interpretation of eddy Reynolds stresses in barotropic ocean jets

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    Rights statement: © Copyright [20 April 2016] American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act September 2010 Page 2 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Act (17 USC §108, as revised by P.L. 94-553) does not require the AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a web site or in a searchable database, or other uses of this material, except as exempted by the above statement, requires written permission or a license from the AMS. Additional details are provided in the AMS Copyright Policy, available on the AMS Web site located at (https://www.ametsoc.org/) or from the AMS at 617-227-2425 or copyrights@ametsoc.org.

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Original languageEnglish
Pages (from-to)2285-2307
Number of pages18
JournalJournal of Physical Oceanography
Issue number8
Early online date20 Apr 2016
Publication statusPublished - 1 Aug 2016


Barotropic eddy fluxes are analysed through a geometric decomposition of the eddy stress tensor. Specifically, the geometry of the eddy variance ellipse, a two-dimensional visualization of the stress tensor describing the mean eddy shape and tilt, is used to elucidate eddy propagation and eddy feedback on the mean flow. Linear shear and jet profiles are analysed and theoretical results are compared against fully nonlinear simulations. For flows with zero planetary vorticity gradient, analytic solutions for the eddy ellipse tilt and anisotropy are obtained that provide a direct relationship between the eddy tilt and the phase difference of a normal mode solution. This allows a straightforward interpretation of the eddy-mean flow interaction in terms of classical stability theory: the initially unstable jet gives rise to eddies which are tilted “against the shear” and extract energy from the mean flow; once the jet stabilises, eddies become tilted “with the shear” and return their energy to the mean flow. For a nonzero planetary vorticity gradient, ray-tracing theory is used to predict ellipse geometry and its impact on eddy propagation within a jet. An analytic solution for the eddy tilt is found for a Rossby wave on a constant background shear. The ray tracing results broadly agree with the eddy tilt diagnosed from a fully nonlinear simulation.

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