The statistical nature of turbulent barotropic ocean jets

Tomos W David,David P Marshall,Laure Zanna

doi:10.1016/j.ocemod.2017.03.008

Abstract

Jets are an important element of the global ocean circulation. Since these jets are turbulent, it is important that they are characterized using a statistical framework. A high resolution barotropic channel ocean model is used to study jet statistics over a wide range of forcing and dissipation parameters. The first four moments of the potential vorticity distribution on contours of time-averaged streamfunction are considered: mean, standard deviation, skewness and kurtosis. A self-similar response to forcing is found in the mean and standard deviation for eastward barotropic jets which exhibit strong mixing barriers; this self-similarity is related to the global potential enstrophy of the flow. The skewness and kurtosis give a behaviour which is characteristic of mixing barriers, revealing a bi/trimodal statistical distribution of potential vorticity with homogenized potential vorticity on each side of the barrier. The mixing barrier can be described by a simple statistical model. This behaviour is shown to be lost in westward jets due to an asymmetry in the formation of zonal mixing barriers. Moreover, when the statistical analysis is performed on eastward jets in a streamfunction following frame of reference, the distribution becomes monomodal. In this way we can distinguish between the statistics due to wave-like meandering of the jet and the statistics due to the more diffusive eddies. The statistical signature of mixing barriers can be seen in more realistic representations of the Southern Ocean and is shown to be an useful diagnostic tool for identifying strong jets on isopycnal surfaces. The statistical consequences of the presence, and absence, of mixing barriers are likely to be valuable for the development of stochastic representations of eddies and their dynamics in ocean models.

Highlights

Ocean jets such as the Gulf Stream, Kuroshio Extension, as well as the jets embedded within the Antarctic Circumpolar Current, represent some of the most turbulent regions of the ocean (e.g., Stammer and Wunsch, 1999)
We have shown that the statistics of potential vorticity in the presence of a mixing barrier are described by mixed distributions, a sum of distributions of random variables
An alternative interpretation of the results presented in this study is that a stochastic parameterization should be implemented in a Lagrangian sense, allowing the noise to be simpler in structure: monomodal instead of the multimodal statistics seen in a Eulerian frame

Summary

Introduction

Ocean jets such as the Gulf Stream, Kuroshio Extension, as well as the jets embedded within the Antarctic Circumpolar Current, represent some of the most turbulent regions of the ocean (e.g., Stammer and Wunsch, 1999) Such jets have an important influence on the large scale circulation of the ocean and atmosphere. More recent studies (Ferrari and Nikurashin, 2010; Klocker et al, 2012) show the suppression of mixing, and the transport of heat and salt, across jets within the Antarctic Circumpolar Current. This suppression of mixing can be attributed to the tendency of strong jets to form mixing barriers, regions of high potential vorticity gradient which eddies have difficulty penetrating

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Discussion

Conclusion