Numerical and theoretical investigation of the variational formulation of a water wave problem
Date of Completion
January 1997
Keywords
Mathematics
Degree
Ph.D.
Abstract
A function $\eta$ is a wave shape if it, along with its streamfunction, satisfies Bernoulli's condition. Thus far only constant, or flat water, shapes are guaranteed to exist. Intuition suggests that there should be non-constant shapes. Here we provide and investigate a variational interpretation of this problem. We numerically study the water wave problem at various vorticities and pressure values. The approach proves well-suited for the implementation of numerical Mountain Pass techniques developed by Choi and McKenna and, using such techniques, we locate numerous non-constant solutions. ^
Recommended Citation
Hill, Sharon H, "Numerical and theoretical investigation of the variational formulation of a water wave problem" (1997). Doctoral Dissertations. AAI9806175.
https://digitalcommons.lib.uconn.edu/dissertations/AAI9806175