A Geometric Interpretation of Southern Ocean Eddy Form Stress

Mads B Poulsen,Markus Jochum,James R Maddison,David P Marshall,Roman Nuterman

doi:10.1175/jpo-d-18-0220.1

Abstract

AbstractAn 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 α, bounded in magnitude by unity. The parameter 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. The eddy efficiency 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. The eddy efficiency 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.

Highlights

The Antarctic Circumpolar Current is embedded in a rich mesoscale eddy field, as readily seen from both satellite altimetry and realistic eddy-resolving model simulations (Storch et al 2012; Roullet et al 2014; Frenger et al 2015; Stewart et al 2015)
The first part examines the structure of Southern Ocean eddy form stress and its geometric representation via the vertical ellipse outlined in sections 2c and 2d, the second part looks into the individual components of the form stress geometry in greater detail, and the third and last part draws together the key findings from the first two parts by presenting estimates of the eddy efficiency a
The vertically and meridionally averaged form stress (Figs. 2a and 2b, respectively) show that it is predominantly positive, consistent with downgradient eddy buoyancy flux and downward transfer of momentum, and is elevated and vertically sustained in several locations along the path of the Antarctic Circumpolar Current. These regions of elevated form stress appear downstream of larger topographic obstacles, such as the Kerguelen Plateau and Drake Passage, and are in alignment with the finding presented in Thompson and Garabato (2014) and Masich et al (2018) that eddy form stress is strong in standing meanders that form in the lee of topography

Summary

Introduction

The Antarctic Circumpolar Current is embedded in a rich mesoscale eddy field, as readily seen from both satellite altimetry and realistic eddy-resolving model simulations (Storch et al 2012; Roullet et al 2014; Frenger et al 2015; Stewart et al 2015). The meanders form when largescale flow navigates submarine topographic obstacles and are associated with elevated deep-reaching eddy kinetic energy (Hallberg and Gnanadesikan 2001; Bischoff and Thompson 2014; Barthel et al 2017) In addition both eddy-resolving models and observations show that the transport of the Antarctic Circumpolar Current is insensitive to a strengthening of the zonal wind stress (Hallberg and Gnanadesikan 2006; Meredith and Hogg 2006; Böning et al 2008; Munday et al 2013; Morrison and Hogg 2013; Marshall et al 2017; Poulsen et al 2018). This is thought to be the consequence of a concurrent increase of eddy form stress which is able to balance the additional surface momentum flux, a phenomenon known as eddy saturation (Straub 1993)

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Discussion

Conclusion