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 language | English |
|---|---|
| Pages (from-to) | 81-94 |
| Number of pages | 14 |
| Journal | Dynamics of Partial Differential Equations |
| Volume | 15 |
| Issue number | 1 |
| Early online date | 14 Dec 2017 |
| DOIs | |
| Publication status | Published - 1 Jan 2018 |
Keywords
- Aperiodic time dependence
- Nearly-integrable Hamiltonian systems
- Shallow-water equations
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Fortunati, A. (2018). Travelling waves over an arbitrary bathymetry: A local stability result. Dynamics of Partial Differential Equations, 15(1), 81-94. https://doi.org/10.4310/DPDE.2018.v15.n1.a4