N-modal steady water waves with vorticity

TL;DR

This paper proves the existence of small-amplitude steady water waves with multiple crests per period, driven by vorticity, using bifurcation theory and dispersion equation roots.

Contribution

It introduces a multidimensional bifurcation approach to establish the existence of complex steady water wave solutions with vorticity.

Findings

Existence of small-amplitude periodic steady waves with multiple crests.

Bifurcation parameters linked to roots of the dispersion equation.

Application of multidimensional bifurcation theory to water waves.

Abstract

The problem for two-dimensional steady gravity driven water waves with vorticity is investigated. Using a multidimensional bifurcation argument, we prove the existence of small-amplitude periodic steady waves with an arbitrary number of crests per period. The role of bifurcation parameters is played by the roots of the dispersion equation.