We describe results from a barotropic vorticity equation model driven by symmetric, double gyre wind forcing. We work in a regime in which the model reaches a state of turbulent equilibrium. The time-average of the statistically steady state exhibits a four gyre structure, in contrast to the usual two gyres associated with symmetric double gyre wind forcing. The four gyre structure is found in model runs using either free slip or super slip boundary conditions, and with either Laplacian or biharmonic mixing for the dissipation. We show that the vorticity budget of both the inner and outer gyres is dominated by a balance between the wind stress curl and the divergence of the eddy potential vorticity flux, with the explicit dissipation playing a much smaller role. The two inner gyres circulate in the same sense as the wind stress curl and are equilibriated, for the most part, by the eddy flux of potential vorticity. The outer gyres, on the other hand, circulate in the opposite sense to the wind stress curl and are driven by the eddy flux of potential vorticity. We show that the gross features of the time-averaged state can be reproduced by a parameterized model in which the divergent part of the potential vorticity flux is represented as a downgradient transfer, and a boundary condition of no normal flux of potential vorticity is applied along the model boundaries. In contrast to the eddy resolving model, the four gyre structure in the parameterized model depends strongly on the choice of side boundary condition.
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