Dispersion relations for steady periodic water waves of fixed mean-depth with two rotational layers

Abstract

The aim of this paper is to obtain the dispersion relation for smallamplitude periodic travelling water waves propagating over a flat bed with a specified mean depth under the presence of a discontinuous piecewise constant vorticity. An analysis of the dispersion relation for a model with two rotational layers each having a non-zero constant vorticity is presented. Moreover, we present a stability result for the bifurcation inducing laminar flow solutions.