A Geometric Interpretation of Southern Ocean Eddy Form Stress

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 that depends on eddy energy and a nondimensional geometric parameter alpha, bounded in magnitude by unity. The parameter alpha 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 alpha in the Southern Ocean and assess its potential to form a basis for parameterization. The eddy efficiency alpha 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. The eddy efficiency is subject to pronounced vertical structure and is maximum at similar to 3-km depth, where eddy buoyancy fluxes tend to be directed most downgradient. Since alpha partly sets the eddy form stress in the Southern Ocean, a parameterization for alpha must reproduce its vertical structure to provide a faithful representation of vertical stress divergence and eddy forcing.