A geometric interpretation of eddy Reynolds stresses in barotropic ocean jets

Talia Tamarin*, James R. Maddison, Eyal Heifetz, David P. Marshall

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Barotropic eddy fluxes are analyzed 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 analyzed 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 that are tilted "against the shear" and extract energy from the mean flow; once the jet stabilizes, 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.

Original languageEnglish
Pages (from-to)2285-2307
Number of pages23
JournalJournal of Physical Oceanography
Issue number8
StatePublished - 1 Aug 2016


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