Steady periodic water waves bifurcating for fixed-depth rotational flows with discontinuous vorticity

TL;DR

This paper proves the existence of small-amplitude steady periodic water waves over a flat bed with fixed depth, considering flows with discontinuous vorticity, using local bifurcation theory.

Contribution

It introduces a novel application of bifurcation theory to flows with discontinuous vorticity, establishing existence results for such water waves.

Findings

Existence of small-amplitude steady periodic water waves with discontinuous vorticity

Application of local bifurcation theory to rotational flows

Validation of wave solutions over fixed-depth beds

Abstract

In this article we apply local bifurcation theory to prove the existence of small-amplitude steady periodic water waves, which propagate over a flat bed with a specified fixed mean-depth, and where the underlying flow has a discontinuous vorticity distribution.