# Solitary waves on rotational flows with an interior stagnation point

## TL;DR

This paper constructs solutions for steady gravity waves with constant negative vorticity, featuring an interior stagnation point and a solitary wave of elevation, advancing understanding of rotational flows with complex internal structures.

## Contribution

It introduces a novel solution construction for steady gravity waves with large negative vorticity, including an interior stagnation point and a critical level curve dividing flow directions.

## Key findings

- Flow has a solitary wave of elevation at the surface.
- Flow contains an interior stagnation point within a bounded domain.
- Flow features a critical level curve connecting stagnation points.

## Abstract

The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Under the assumption that the vorticity is a negative constant whose absolute value is sufficiently large, we construct a solution with the following properties. The corresponding flow is unidirectional at infinity and has a solitary wave of elevation as its upper boundary; under this unidirectional flow, there is a bounded domain adjacent to the bottom, which surrounds an interior stagnation point and is divided into two subdomains with opposite directions of flow by a critical level curve connecting two stagnation points on the bottom.