Dispersion Relations for Fixed Mean-Depth Steady Periodic Water Waves with Affine Vorticities

Abstract

In this paper, we consider two-dimensional steady periodic equatorial water waves of small amplitude, which propagate over a flat bed and beneath a free surface. In particular, we assume that the flow has a fixed mean-depth. After analyzing the existence of Laminar solution, we obtain the dispersion relations for the affine vorticity distribution.