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This paper formulates tracer stirring arising from the Gent–McWilliams (GM) eddy-induced transport in terms of a skew-diffusive flux. A skew-diffusive tracer flux is directed normal to the tracer gradient, which is in contrast to a diffusive tracer flux directed down the tracer gradient. Analysis of the GM skew flux provides an understanding of the physical mechanisms prescribed by GM stirring, which is complementary to the more familiar advective flux perspective. Additionally, it unifies the tracer mixing operators arising from Redi isoneutral diffusion and GM stirring. This perspective allows for a computationally efficient and simple manner in which to implement the GM closure in z-coordinate models. With this approach, no more computation is necessary than when using isoneutral diffusion alone. Additionally, the numerical realization of the skew flux is significantly smoother than the advective flux. The reason is that to compute the skew flux, no gradient of the diffusivity or isoneutral slope is taken, whereas such a gradient is needed for computing the advective flux. The skew-flux formulation also exposes a striking cancellation of terms that results when the GM diffusion coefficient is identical to the Redi isoneutral diffusion coefficient. For this case, the horizontal components to the tracer flux are aligned down the horizontal tracer gradient, and the resulting computational cost of Redi diffusion plus GM skew diffusion is roughly half that needed for Redi diffusion alone.

Gent and McWilliams (1990, GM hereafter) and Gent et al. (1995, hereafter GWMM) suggested a closure for

the tracer equation to be used in ocean models. With this closure, certain adiabatic stirring effects from ocean mesoscale eddies are encapsulated by a divergence-free eddy-induced velocity. The GM velocity incorporates that aspect of baroclinic eddies representing the transfer of available potential energy to eddy kinetic energy. It has been noted in various atmospheric contexts (e.g., Plumb 1979; Plumb and Mahlman 1987) that eddy-induced transport velocities are generally equivalent to antisymmetric components in the tracer mixing tensor. This mixing will not alter any of the tracer moments as long as no-normal flow, or equivalently no-flux, boundary conditions are applied to the corresponding advective

or skew-diffusive tracer flux. In this sense, the mixing is nondissipative, reversible, and sometimes referred

to as ‘‘stirring’’ (Eckart 1948).

Gent and McWilliams (1990, GM hereafter) and Gent et al. (1995, hereafter GWMM) suggested a closure for

the tracer equation to be used in ocean models. With this closure, certain adiabatic stirring effects from ocean mesoscale eddies are encapsulated by a divergence-free eddy-induced velocity. The GM velocity incorporates that aspect of baroclinic eddies representing the transfer of available potential energy to eddy kinetic energy. It has been noted in various atmospheric contexts (e.g., Plumb 1979; Plumb and Mahlman 1987) that eddy-induced transport velocities are generally equivalent to antisymmetric components in the tracer mixing tensor. This mixing will not alter any of the tracer moments as long as no-normal flow, or equivalently no-flux, boundary conditions are applied to the corresponding advective

or skew-diffusive tracer flux. In this sense, the mixing is nondissipative, reversible, and sometimes referred

to as ‘‘stirring’’ (Eckart 1948).

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