Water wave problem with inclined walls
Abstract
We study free surface water waves in a 2-D symmetric triangular channel with sides that have a 45o slope. We develop models for small amplitude nonlinear waves, extending earlier studies that have considered the linearized problem. We see that a combination of heuristic small amplitude expansions lead to a relatively simple system that we then use to study interactions of low frequency modes. The formalism relies on an explicit construction of the normal modes of the linear problem and a new way to represent the free surface. We argue that the construction can be applied to more general geometries. We also examine the structure and some dynamical features of spectral truncations for the lowest even modes.
Cite
@article{arxiv.2205.01585,
title = {Water wave problem with inclined walls},
author = {P. Panayotaros and R. M. Vargas-Magaña},
journal= {arXiv preprint arXiv:2205.01585},
year = {2022}
}
Comments
This is a revised version of our manuscript: Water wave problem with inclined walls. The paper proposes a new way to define the free surface that solves a number of problems arising in domains with inclined walls in an elegant way. Our main goal is to show how to combine this definition and the equations of motion to obtain simplified models and physically interesting results