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Fluids 2017, 2(4), 54; doi:10.3390/fluids2040054

The Eddy Diffusivity in Barotropic β-Plane Turbulence

Department of the Geophysical Sciences, The University of Chicago, Chicago, IL 60637, USA
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Received: 1 September 2017 / Revised: 4 October 2017 / Accepted: 6 October 2017 / Published: 12 October 2017
(This article belongs to the Collection Geophysical Fluid Dynamics)
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Abstract

Geostrophic turbulent eddies play a crucial role in the oceans, mixing properties such as heat, salt, and geochemical tracers. A useful reduced model for geostrophic turbulence is barotropic (2D) turbulence. The focus of this study is on 2D β -plane turbulence with quadratic drag, which, although arguably the most realistic barotropic model of ocean turbulence, has remained unexplored thus far. We first review and test classical scaling arguments for the eddy diffusivity in three regimes: the strong friction limit, the weak friction/strong β limit, and a transition regime. We then develop a generalized theory by parameterizing the nonlinear eddy–eddy interactions as a stochastic process, which leads to an analytical solution for the eddy diffusivity spectrum, whose integral yields a “bulk” diffusivity. The theory successfully predicts the smooth transition of diffusivity across the three regimes, and echoes with the recent argument that eddy phase propagation relative to the mean flow suppresses the eddy diffusivity. Moreover, the generalized theory reduces to the classical scaling arguments in both the strong friction and strong β limits, which has not been clear from the previous work on diffusivity suppression by flow-relative phase propagation. View Full-Text
Keywords: barotropic turbulence; mixing length theory; eddy parameterization; eddy diffusivity; mixing suppression barotropic turbulence; mixing length theory; eddy parameterization; eddy diffusivity; mixing suppression
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Kong, H.; Jansen, M.F. The Eddy Diffusivity in Barotropic β-Plane Turbulence. Fluids 2017, 2, 54.

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