The Relation 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 relation between the wind-stress distribution and its temporal correlations and the statistics of the open ocean currents. We find that temporally long-range correlated wind results in currents whose statistics is proportional to the wind-stress statistics. On the other hand, short-range correlated wind leads 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 find 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.; A map of the correlation time (in days) of the wind-stress magnitude. We define the correlation time as the time at which the normalized auto-correlation function first drops below 1/e. Clearly, there is a large variability in the correlation time. One can also notice the remarkably shorter correlation time overland compared with that over the ocean (except for the polar regions). The map is based on the NCEP/NCAR reanalysis six-hourly wind data for the period of 1993-2010 (Kalnay et al, 1996). The spatial resolution of the data is 2.5°× 2.5°. Other definitions of the correlation time yield qualitatively the same results. The black contour line indicates a one-day correlation time, and the white line indicates the coast line. A grid (light blue lines) of 30°× 30° was superimposed on the map. ; The scaled second moment of the current amplitude versus the constant wind-stress duration, T (in units of 1 over the Coriolis frequency, f) . The different lines correspond to different values of the bottom drag parameter, r.