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 |
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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