On periodic geophysical water flows with discontinuous vorticity in the equatorial f-plane approximation

We are concerned here with geophysical water waves arising as the free surface of water flows governed by the f-plane approximation. Allowing for an arbitrary bounded discontinuous vorticity, we prove the existence of steady periodic two-dimensional waves of small amplitude. We illustrate the local bifurcation result by means of an analysis of the dispersion relation for a two-layered fluid consisting of a layer of constant non-zero vorticity gamma(1) adjacent to the surface situated above another layer of constant non-zero vorticity gamma(2) not equal gamma(1) adjacent to the bed. For certain vorticities gamma(1), gamma(2), we also provide estimates for the wave speed c in terms of the speed at the surface of the bifurcation inducing laminar flows. This article is part of the theme issue 'Nonlinear water waves'.