Surface waves with rotation: An exact solution

The Gerstner solution (1809) for waves on the surface of a semi-infinite homogeneous fluid is extended for an incompressible vertically stratified fluid in a rotating system. For oceanic surface waves on the earth the frequency and vertical wave number differ only negligibly from their nonrotating values. The particle orbits, while still circular, now lie in a plane slightly tilted from the vertical. This has important consequences when one considers the second-order drift currents associated with surface waves. These waves, which are rotational, can be generated by irrotational forces in a rotating system.