Wind Action on a Shallow Sea: Some Generalizations of Ekman’s Theory

In 1923 Ekman developed a theory for the sea-level changes produced in a deep sea by the action of a steady wind. In the present paper the theory has been extended to a shallow sea, for which the Ekman “depth of frictional influence” d is comparable to the actual depth h. It is pointed out that the wind-stress divergence may be of the same importance as the wind-stress curl in this case.

The theory is furthermore extended to the transient case. It is demonstrated how the velocity profile and the flow can be expressed in terms of the local time-histories of the wind-stress and the surface slope, and a single integro-differential equation is derived for the sea-level elevation. This equation could possibly be used for prediction of meteorologic tides and storm surges.