Equatorial transport driven by periodically rotating wind stress

The wind-driven transport on the equator is studied, analytically and numerically, in the case where the wind stress vector rotates periodically. The analysis of the Lagrangian model is enabled by substituting the pseudo angular momentum for the zonal velocity in the nonlinear, time-dependent, governing equations. For small-amplitude wind forcing, our results predict first-order oscillatory motions in the meridional and zonal directions at the inertial and forcing frequencies and their harmonics. These first-order oscillations are accompanied by second-order drift in the zonal direction, directed eastward or westward depending on the forcing frequency. There exist resonant frequencies at which the long-term averaged zonal speed is very fast, reaching 0.5 ms−1, while the oscillatory motion is greatly reduced and the water column moves mainly eastward, even though the wind forcing has no dominant direction.