The effects of the stochastic component of the large-scale wind on the climatological mean of the nonlinear ocean circulation are studied, using a set of numerical solutions for the single-layer, quasi-geostrophic equation in a closed basin with a flat bottom. In the absence of a steady wind, the purely stochastic wind is found to drive the solutions toward a nonlinear mean flow similar to that of the free system (i.e. without forcing and dissipation). This equilibrium mean flow (Fofonoff flow), is predicted by statistical mechanics and is characterized by a westward interior closed by inertial boundary layers along the coast. When a steady component of the wind is present, the effects of the stochastic wind depend on the geometry of the steady wind. If the steady wind is compatible with Fofonoff flow, the stochastic wind tends to reinforce the Fofonoff-like mean solution obtained with the steady wind alone. When the steady wind opposes Fofonoff flow, the contribution of the stochastic wind does not increase the energy of the mean solution, but instead tends to change the spatial structure of the mean flow. An example of steady wind opposing Fofonoff flow is the classical double-gyre wind, often used to represent the realistic mean wind in mid-latitude ocean regions. We study the double-gyre wind case in detail. The stochastic wind is found to weaken the recirculating regions and the meandering jet between the two gyres, and the homogenization of potential vorticity in the recirculations is inhibited. These changes are explained in terms of increased mixing of the probability density in phase space due to the stochastic wind, causing an increased tendency toward the equilibrium state predicted by statistical mechanics.