Wave akin to the Gerstner type in a rotating fluid (Q1324612)

In rotating fluids the existence of exact solutions expressing a form of wave motions similar to that of Gerstner is not a priori questionable. Effectively explicit solutions in Lagrangian form, representing rotational waves of finite amplitude in deep water (infinite depth), are investigated briefly. A first solution extends that of Gerstner by including the rotation. A second solution with no transverse velocity describes nonlinear Kelvin type waves, and a third solution represents nonlinear edge waves on a sloping plane bottom. It is observed that the dispersion relations for these waves are just the same as for linear waves of infinitesimal amplitude.