Power Input Generated by a Linear Wind Field on Circular and Elliptical Ocean Vortices

The wind power input exerted by the lower atmosphere on the upper ocean is investigated theoretically. The formulation depends on the wind stress parameterization, which is usually based on the relative speed between the two fluids and implies that oceanic motions alter the surface wind stress (current feedback effect). This study examines the power input generated by a linear wind field over mesoscale cyclonic and anticyclonic vortices. It is demonstrated unambiguously that the power input over idealized circular and elliptical vortices is a linear function of the wind curl and a quadratic function of the vortex strength. Furthermore, the power input in elongated vortices depends on their orientation with respect to the wind direction. Overall, the results provide arguments for discussing current feedback effects in the presence of a nonuniform wind and noncircular vortices. In all cases, for instance, the wind power input (positive or negative) is lower than in the case when the wind stress is based on the absolute wind velocity (no current feedback), in agreement with previous studies.