Steady water waves with multiple critical layers

TL;DR

This paper constructs small-amplitude steady periodic water waves with multiple critical layers and various crest-trough configurations, advancing understanding of complex wave structures with vorticity in finite-depth settings.

Contribution

It introduces the first construction of small-amplitude steady water waves featuring multiple critical layers and complex crest-trough arrangements with vorticity.

Findings

Existence of waves with arbitrarily many critical layers.

Presence of waves with multiple crests and troughs per period.

Extension of wave theory to include complex vorticity-induced structures.

Abstract

We construct small-amplitude periodic water waves with multiple critical layers. In addition to waves with arbitrarily many critical layers and a single crest in each period, two-dimensional sets of waves with several crests and troughs in each period are found. The setting is that of steady two-dimensional finite-depth gravity water waves with vorticity.