Symmetric finite-amplitude rotational water waves.

Two forms of a two-dimensional streamfunction solution for symmetric periodic water waves on a fluid with a vertical distribution of vorticity are presented. The magnitude of the vorticity varies linearly with the magnitude of the streamfunction while remaining constant on a particular streamline. The analysis utilizes a numerical perturbation technique, which converges rapidly to a wave of given height and period in water of a specfied depth with a given vorticity distribution. Computed results show the influence of the vorticity on the wavelength and crest elevation of the wave. (A)