Ekman Theory with Damping

Abstract: The observed Ekman spirals in the ocean are always "flatter" than that predicted by the classic theory. We propose that the universal flattening of Ekman spiral is mainly due to the damping associated with turbulent dissipation. Analytical solutions and numerical simulations show convincingly a better fitting between the new theory and observations. Most importantly, the new theory indicates that the damping can lead to weakened Ekman transport and pumping, with the latter not only driven by the curl but also the divergence of wind stress. Under a modest damping, the Ekman transport along 26.5{\deg}N will be ~0.4 Sv (12%) smaller than that predicted by the classic theory. Hence, the damping due to turbulent dissipation can noticeably affect the wind-driven circulation in the upper ocean.