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ABSTRACT
The time-mean effects of eddies are studied in a model based on the Parsons-Veronis-Huang-Flierl models of the wind-driven gyre. Much of the analysis used for the steady solutions carries over if the model is cast in terms of the thickness-weighted mean velocity, because then mass transport is nondivergent in the absence of diabatic forcing. The model exemplifies the use of residual mean theory to simplify analysis.
A result of the analysis is a boundary layer width in the case of a rapid upper-layer flow and weak lower-layer flow. This boundary layer width is comparable to an eddy mixing length when the typical eddy velocity is taken to be the long Rossby wave phase speed.
Further analysis of the model illustrates important aspects of eddy behavior, model sensitivity to eddy fluxes, and model sensitivity to frictional parameters.
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1. Introduction
The ubiquitous mesoscale eddies in the ocean affect the transport and structure of tracers: salt, potential temperature, potential density, and potential vorticity (PV). The turbulent character of these eddies makes for few tractable observational, analytical, and numerical approaches. Formal mathematical treatments of eddy fluxes have revealed that careful manipulation of the definition of an eddy may provide advantages in capturing the eddy-mean flow interaction. The Transformed Eulerian Mean (TEM: e.g., Andrews et al. 1987; Vallis 2006) and Generalized Lagrangian Mean (GLM; Andrews and Mclntyre 1978) frameworks are two examples.
Here the temporal residual mean formulation (TRM; McDougall and Mcintosh 2001) is used to formulate a model consistent with the mean density structure of the ocean while retaining some important effects of time-dependent eddies. In an isopycnal-coordinate model, the TRM velocity is simply the thickness-weighted mean velocity, and the layer mass and tracer transports are natural. The TRM approach has been used successfully to study eddy-mean flow interactions in the atmosphere (Andrews et al. 1987). Here we show that similar advantages arise in the study of gyre circulations in enclosed domains. In particular we use the TRM formalism to include eddy feedbacks in models akin to Parsons (1969) and later extensions by other investigators.
Unlike much of the recent literature, this paper does not provide detailed maps of eddy diffusivities or viscosities: instead the TRM Parsons model compellingly illustrates the roles...