Recently a new class of coarse-grained equations, known as a models, have b
een proposed for the mean motion of an ideal incompressible fluid. The use
of one such model to represent the time-mean component of a turbulent beta
-plane circulation characterized by potential vorticity mixing is considere
d. In particular, the focus is on the wind-driven circulation in a shallow
ocean basin, a problem well studied as a prototype of more realistic ocean
dynamics. The authors demonstrate the ability of an alpha model to reproduc
e qualitatively the structure of a four-gyre circulation that forms (in the
time mean) when the barotropic vorticity equation is driven by a symmetric
, double-gyre wind forcing, and when the dissipation is weak. This is offer
ed as a first step in assessing the utility of the alpha -model approach to
simulating more complex geophysical flows.