# Publications by David Marshall

## A geometric interpretation of Southern Ocean eddy form stress

Journal of Physical Oceanography American Meteorological Society **49** (2019) 2553-2570

An interpretation of eddy form stress via the geometry described by the Eliassen-Palm flux tensor is explored. Complimentary to previous works on eddy Reynolds stress geometry, this study shows that eddy form stress is fully described by a vertical ellipse, whose size, shape and orientation with respect to the mean-flow shear determine the strength and direction of vertical momentum transfers. Following a recent proposal, this geometric framework is here used to form a Gent-McWilliams eddy transfer coefficient which depends on eddy energy and a non-dimensional geometric parameter α, bounded in magnitude by unity. α expresses the efficiency by which eddies exchange energy with baroclinic mean-flow via along-gradient eddy buoyancy flux - a flux equivalent to eddy form stress along mean buoyancy contours. An eddy-resolving ocean general circulation model is used to estimate the spatial structure of α in the Southern Ocean and assess its potential to form a basis for parameterization. α averages to a low but positive value of 0.043 within the Antarctic Circumpolar Current, consistent with an inefficient eddy field extracting energy from the mean-flow. It is found that the low eddy efficiency is mainly the result of that eddy buoyancy fluxes are weakly anisotropic on average. α is subject to pronounced vertical structure and is maximum at ∼ 3 km depth where eddy buoyancy fluxes tend to be directed most downgradient. Since α partly sets the eddy form stress in the Southern Ocean, a parameterization for α must reproduce its vertical structure to provide a faithful representation of vertical stress divergence and eddy forcing.

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