Reply on RC2

Abstract. The seminal, Ekman (1905)’s, f-plane theory of wind driven transport at the ocean surface is extended to the β-plane by substituting the pseudo angular momentum for the zonal velocity in the Lagrangian equation. The addition of the β term implies that equations become nonlinear, which greatly complicates the analysis. Though rotation relates the momentum equations in the zonal and the meridional directions, the transformation to pseudo angular momentum greatly simplifies the longitudinal dynamics, which yields a clear description of the meridional dynamics in terms of a slow drift compounded by fast oscillations, which can then be applied to describe the motion in the zonal direction. Both analytical expressions and numerical calculations underscore the critical role of the equator in determining the trajectories of water columns forced by eastward directed wind stress even when the water columns are far from the equator. Our results demonstrate that the averaged motion in the zonal direction is highly dependent on the meridional oscillations and for some initial conditions can be as large as the meridional mean motion.