The Eddy Diffusivity in Barotropic β-Plane Turbulence
Department of the Geophysical Sciences, The University of Chicago, Chicago, IL 60637, USA
Author to whom correspondence should be addressed.
Received: 1 September 2017 / Revised: 4 October 2017 / Accepted: 6 October 2017 / Published: 12 October 2017
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
-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
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
limits, which has not been clear from the previous work on diffusivity suppression by flow-relative phase propagation.
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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MDPI and ACS Style
Kong, H.; Jansen, M.F. The Eddy Diffusivity in Barotropic β-Plane Turbulence. Fluids 2017, 2, 54.
Kong H, Jansen MF. The Eddy Diffusivity in Barotropic β-Plane Turbulence. Fluids. 2017; 2(4):54.
Kong, Hailu; Jansen, Malte F. 2017. "The Eddy Diffusivity in Barotropic β-Plane Turbulence." Fluids 2, no. 4: 54.
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