109 A New Approach to the Oceanic Meso-Scale Eddy Parameterization Problem

Tuesday, 27 June 2017
Salon A-E (Marriott Portland Downtown Waterfront)
Rémi Tailleux, University of Reading, Reading, United Kingdom

The parameterisation of meso-scale eddies is widely regarded as a vital component of non-eddy resolving numerical ocean models. Its success lies in naturally eliminating a number of undesirable features in early numerical ocean models, such as the spurious upwelling in western boundary currents or excessive deep water formation in the Southern Ocean. From a dynamical viewpoint, the meso-scale eddy parameterisation is also key for setting up the strength of the Antarctic Circumpolar Current and its response to changing winds, owing to its control of the isopycnal slopes that control the ACC via the thermal wind relation. From a physical viewpoint, the meso-scale eddy parameterisation is generally interpreted as causing an eddy-induced advection, which combines with the Eulerian mean velocity to form a residual velocity. As a result, the meso-scale eddy parameterisation does not dissipate the variance of temperature and salinity, but is usually constrained to act as an adiabatic sink of available potential energy. From a practical viewpoint, the meso-scale eddy parameterisation can be formulated in terms of a skew-symmetric tensor, whose turbulent mixing coefficient is often assumed to be equal or linked to the isopycnal turbulent mixing coefficient used in the symmetric part of the rotated diffusion tensors. For the widely used Gent and McWilliams parameterisation, the velocity potential entering the skew-symmetric part of the rotated diffusion tensor is usually assumed to be perpendicular to the locally defined neutral density gradient. There has been some discussion, however, about how best formulate a first-principles construction of the meso-scale eddy parameterisation, and most notably whether it should invoke PV mixing arguments, or be based on the budget of available potential energy and Lorenz energy cycle. There has also been some discussion about whether the standard GM parameterisation could be missing some physics, related to the suggestion that it should be augmented by a term proportional to the neutral density gradient. This new term involves a turbulent mixing coefficient that has been found to be as large as the GM mixing coefficient, but its physical origin and function are not fully understood. The purpose of this work is to show that if the same rotated diffusion tensor is assumed for both temperature and salinity, then both its skew-symmetric and symmetric parts can be entirely expressed in terms of the turbulent heat and salt fluxes, or equivalently in terms of density and spiciness (density-compensated T/S) turbulent fluxes. This general and exact result confirms that the standard GM is missing a number of terms, whose physical nature will be discussed and clarified. It also provides a first-principle justification for the link between the turbulent mixing coefficients entering the general expression for the skew-symmetric part of the rotated diffusion tensor and the symmetric part.

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