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Baylor Fox-Kemper and Raffaele Ferrari

the strictly adiabatic conditions there. In the real ocean some interior diapycnal transformation results from diffusion–mesoscale interaction, as Radko and Marshall (2004) also suggest. In TRM this latter physical effect, which produces w 1− in the thickness-weighted mean Eq. (3) and a corresponding vortex stretching term f w 1− in (49) , is distinguished from the kinematic effect of f w̃ 1− that appears only if the Eulerian mean velocity is used. Similarly, the depth

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K. Shafer Smith and John Marshall

statistics. A crucial result of our study is that mesoscale eddy mixing is, indeed, peaked at a depth of about 1 km in the core of the ACC. Moreover, mixing is found to be strongly depth dependent, and the diffusivities for buoyancy and potential vorticity are found to be quite different, both in magnitude and structure (basic kinematics show that, when mixing is not constant in the vertical, diffusivities of buoyancy and PV cannot be the same). An effective diffusivity calculation ( Nakamura 1996

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R. M. Samelson

that supports a Stommel ( e − βx / r ) western boundary layer, and τ x and τ y are the zonal and meridional components of the imposed kinematic wind stress. A presumption of the formulation is that the warm-water branch of the middepth cell lies above the main internal thermocline and is subject to the direct action of wind, at least in the sense of ventilated thermocline theory ( Luyten et al. 1983 ; Samelson and Vallis 1997 ), which is represented here in its most simplistic form by a single

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