Steady water waves with multiple critical layers: interior dynamics

TL;DR

This paper investigates small steady water waves with multiple critical layers, revealing complex internal vortex structures and demonstrating the possibility of arbitrarily many such layers with distinct features at different depths.

Contribution

It introduces the existence of multiple critical layers with cat's-eye vortices in steady water waves, expanding understanding of internal fluid dynamics in rotational flows.

Findings

Multiple critical layers with vortices are possible within finite-depth fluids.

Vorticity varies linearly with the stream function.

Different structures are observed at various fluid levels.

Abstract

We study small-amplitude steady water waves with multiple critical layers. Those are rotational two-dimensional gravity-waves propagating over a perfect fluid of finite depth. It is found that arbitrarily many critical layers with cat's-eye vortices are possible, with different structure at different levels within the fluid. The corresponding vorticity depends linearly on the stream function.