Some Remarks Regarding the Solution of Stokes and Rayleigh for Surface Waves of Finite Amplitude

I.

An exact solution of the hydrodynamic equations was found by Gerstner, but the waves represented by Gerstner's solution are not irrotational such that they cannot be generated from rest by conservative forces in an ideal fluid. Stokes found an approximate solution for the irrotational case where the surface profile of the waves was represented by the equation y = βe^ky cos kx but in this case the surface condition of constant pressure was only satisfied approximately.