Results will be presented of a study on the interaction of noise and nonlinear dynamics in a quasi-geostrophic model of the wind-driven ocean circulation. The recently developed framework of dynamically orthogonal field theory is used to determine the statistics of the flows which arise through successive bifurcations of the system as the ratio of forcing to friction is increased. Focus will be on the understanding of the role of the spatial and temporal coherence of the noise in the wind-stress forcing. For example, when the wind-stress noise is additive and temporally white, the statistics of the stochastic ocean flow does not depend on the spatial structure and amplitude of the noise. This implies that a spatially inhomogeneous noise forcing in the wind stress field only has an effect on the dynamics of the flow when the noise is temporally colored. The latter kind of stochastic forcing may cause more complex or more coherent dynamics depending on its spatial correlation properties.