Wind-induced currents directed to the left of the wind in the northern hemisphere: An elementary explanation and its historical background

Abstract

Every beginning student of geophysical fluid dynamics knows that steady-state wind-driven currents are directed to the right of the wind in the northern hemisphere. In contrast, the fact that wind-induced currents may under some specific conditions be of the opposite direction is mentioned in only a few papers. Here, a succession of simple explicit solutions is used to illustrate that the wind varying at subinertial frequencies always generates currents directed to its right, whereas at superinertial frequencies the wind rotating clockwise (counterclockwise) coincides with currents directed to its left (right). The difference is related to a dynamics differing in the two frequency bands. At subinertial frequencies, friction is primarily balanced by the Coriolis acceleration, and therefore the currents vary in phase with the wind while being directed to its right. At superinertial frequencies, the primary balance is between friction and local acceleration, implying that the currents lag behind the wind that causes them while pointing down the forcing. The former dynamic regime was originally considered by Vagn Walfrid Ekman (in 1905), the latter by Karl Jakob Zöppritz (in 1878). The destiny of the two contributions, however, was completely different: Ekman’s is widely appreciated today, whereas Zöppritz’s is rarely mentioned. Although Zöppritz’s findings were adversely influenced by his consideration of the laminar rather than turbulent viscosity, his neglect of the Coriolis acceleration was acceptable and his solution therefore formally correct at superinertial frequencies.