Travelling waves over an arbitrary bathymetry: A local stability result

Alessandro Fortunati*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

1 Citation (Scopus)
199 Downloads (Pure)

Abstract

The problem of a travelling wave in a semi-infinite channel over an arbitrary quasi-flat bathymetry 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 a perturbation which is aperiodic in time. The obtained model provides a natural example in the context of the aperiodically time-dependent Hamiltonian systems studied in Fortunati and Wiggins (2016) and the local stability of the perturbed streamlines is obtained as a consequence of this theory. The proofs use the tools of Perturbation Theory in the real-analytic setting.

Original languageEnglish
Pages (from-to)81-94
Number of pages14
JournalDynamics of Partial Differential Equations
Volume15
Issue number1
Early online date14 Dec 2017
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • Aperiodic time dependence
  • Nearly-integrable Hamiltonian systems
  • Shallow-water equations

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