# Explicit equations for two-dimensional water waves with constant vorticity

## TL;DR

This paper derives exact equations for 2D water waves with constant vorticity over uneven bottoms and introduces a highly accurate numerical method for solving these equations.

## Contribution

It provides a novel, compact formulation of water wave equations with constant vorticity and develops an efficient numerical approach.

## Key findings

- Exact conformal equations for water waves with vorticity
- High-accuracy numerical method demonstrated
- Applicable to arbitrary bottom profiles

## Abstract

Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate numerical method for this problem is developed.