The Eddy Diffusivity in Barotropic β-Plane Turbulence

Hailu Kong,Malte Jansen

doi:10.3390/fluids2040054

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.

Highlights

Geostrophic turbulent eddies are crucial in geophysical fluids for the transport and mixing of properties
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
Adopting the linearization technique used in FN10, we have developed a generalized theory for the full diffusivity spectrum in barotropic turbulence, whose integral yields a “bulk” diffusivity that agrees with simulations across all three regimes

Summary

Introduction

Geostrophic turbulent eddies are crucial in geophysical fluids for the transport and mixing of properties. In the earth’s oceans, they cannot be fully resolved by current global climate models, due to their relatively small size [1]. Their representation has to rely on adequate eddy parameterization schemes [2,3,4]. A common practice to parameterize sub-grid scale turbulence is to employ a diffusive closure, which assumes that unresolved eddy fluxes can be related to the large scale mean gradient via an eddy diffusivity. The eddy parameterization problem comes down to expressing the eddy diffusivity based on resolvable large scale quantities. This paper aims to improve parameterizations for the eddy diffusivity by studying 2D turbulence as a reduced model for geostrophic turbulence

Objectives

Results

Conclusion