The relationship between the statistics of open ocean currents and the temporal correlations of the wind stress

We study the statistics of wind-driven open ocean currents. Using the Ekman layer model for the integrated currents, we investigate analytically and numerically the relationship between the wind-stress distribution and its temporal correlations and the statistics of the open ocean currents. We found that temporally long-range correlated winds result in currents whose statistics is proportional to the wind-stress statistics. On the other hand, short-range correlated winds lead to Gaussian distributions of the current components, regardless of the stationary distribution of the winds, and therefore to a Rayleigh distribution of the current amplitude, if the wind stress is isotropic. We found that the second moment of the current speed exhibits a maximum as a function of the correlation time of the wind stress for a non-zero Coriolis parameter. The results were validated using an oceanic general circulation model.