Capillary-Gravity Water Waves: Modified Flow Force Formulation

TL;DR

This paper introduces a new formulation for capillary-gravity water waves using a modified flow force function, proving the local existence of small amplitude waves through bifurcation theory.

Contribution

It develops a novel formulation based on a modified flow force function and establishes the existence of small amplitude wave solutions.

Findings

New flow force formulation for capillary-gravity waves

Proof of local existence of small amplitude waves

Application of bifurcation theory to water wave problem

Abstract

The classical irrotational capillary-gravity water wave problem described by the Euler equations with a nonlinear free surface boundary condition over a flat bed is considered. A modified flow force has been defined and a new formulation of capillary-gravity waves in the framework of the modified flow force function has been developed. Using bifurcation theory, the local existence of waves of small amplitude is proved.