On the transient state of wind-driven coastal currents

A solution to the transient state of Ekman’s elementary current system is presented. The forcing consists of a suddenly imposed wind, directed along an infinite straight coast. The problem is identical to that treated by Ekman (1905) and it is shown that Ekman’s solution is valid only at very great distance from the coast, or at extended times. The present solution reveals the existence of two time scales and shows that the main response is confined to a coastal region where it is characterized by the “spin up time”. The width of this region is of the order of the Rossby radius of deformation. At increasing distance from the coast, the response time approaches the diffusive time scale obtained by Ekman.