New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

TL;DR

This paper derives new exact relations and equations for steady irrotational two-dimensional gravity and capillary surface waves, including a physical plane version of the Babenko equation, enhancing understanding of wave behavior.

Contribution

It introduces novel exact relations and a Babenko-type equation for free surface waves using holomorphic properties and boundary transformations.

Findings

Derived new exact relations for free surface waves.

Obtained a physical plane counterpart of the Babenko equation.

Enhanced analytical tools for studying gravity-capillary waves.

Abstract

Steady two-dimensional surface capillary-gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained.