On the Theoretical Form of Ocean Swell. On a Rotating Earth

In the discussion of the form of ocean swell the waves studied by Gerstner’ (1802) and Stokes (1847) have received particular attention. In Gerstner waves each fluid particle describes a circle about a fixed point. Their mathematical properties are very simple, but they cannot be generated from rest by conservative forces. On the other hand, Stokes waves can be generated from rest by conservative forces. There is a surface drift associated with Stokes-waves; but the mathematical difficulties are considerable. It has been customary to consider swell as a train of Stokes waves. One of the fundamental assumptions underlying these theories is that the waves are moving on a non-rotating Earth. It is now shown that if the curvature of the Earth can be neglected, the effect of the Earth's rotation makes swell waves in their stationary state differ very little from Gerstner waves. The work suggests that in the general case each particle moves approximately in a horizontal circle of inertia as well as in the nearly vertical Gerstner motion;. the diameter of the inertia circles is greatest at the surface, where it may be several hundred metres, and the period of revolution is half a pendulum day (equal to 12 cosec ø hours, where ø is the latitude). Except for this circular movement there is no mass transport, and thus. there is no ground for supposing that ocean drift currents are due to fluid transport with the waves. On the other hand, waves appear to provide a reasonable mechanism for the generation of inertia currents which have been frequently observed.