Travelling waves over an arbitrary bathymetry: a perturbation theory approach
Dynamical Systems
2018-02-12 v1
Abstract
The problem of a travelling wave over an arbitrary quasi-flat bathymetry in a semi infinite channel is studied in the shallow-water formulation. It is shown how the streamfunction can be cast, in the vicinity of an elliptic equilibrium for the fluid flow, in the form of a nearly-integrable non-autonomous Hamiltonian with aperiodic time dependence. The proofs use the tools of perturbation theory in the real-analytic setting. The obtained Hamiltonian provides a natural example in the context of the aperiodically time-dependent Hamiltonian systems studied in Fortunati and Wiggins (2016). Some key properties of the system at hand, such as the stability, can be addressed as a consequence of this theory.
Keywords
Cite
@article{arxiv.1707.01402,
title = {Travelling waves over an arbitrary bathymetry: a perturbation theory approach},
author = {Alessandro Fortunati},
journal= {arXiv preprint arXiv:1707.01402},
year = {2018}
}