This paper presents analytical and numerical results for a class of turbulence closure models called ''alpha models,'' in which Lagrangian averaging and turbulence closure assumptions modify the Eulerian nonlinearity. The alpha models are investigated in the setting of the barotropic, double-gyre circulation in an ocean basin. Two variants of the alpha models for the barotropic vorticity (BV) equation are found to produce the correct four-gyre configuration for the mean barotropic circulation in numerical simulations performed at a resolution 4 times as coarse as that required in a resolved BV model. These are the BV- model and the BV-Leray- model. However, at a resolution 8 times as coarse, only the BV- model produces the proper four-gyre configuration. Thus, the combination of modified nonlinearity and viscous dissipation (the viscosity is the same in all of the runs) in the BV- model is found to provide a promising approach to modeling the mean effects of unresolved mesoscale (subgrid scale) activity in this problem.
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Holm et al. (2003) studied this question.