Gravity water flows with discontinuous vorticity and stagnation points

TL;DR

This paper constructs small-amplitude steady periodic gravity water waves with discontinuous vorticity layers and stagnation points, analyzing their streamline patterns and flow structure.

Contribution

It introduces a novel construction of steady gravity water waves with layered vorticity and stagnation points, expanding understanding of complex flow configurations.

Findings

Existence of small-amplitude steady periodic waves with layered vorticity.

Flow patterns include stagnation points and distinct streamline configurations.

Flows consist of two layers with different constant vorticities.

Abstract

We construct small-amplitude steady periodic gravity water waves arising as the free surface of water flows that contain stagnation points and possess a discontinuous distribution of vorticity in the sense that the flows consist of two layers of constant but different vorticities. We also describe the streamline pattern in the moving frame for the constructed flows.