Transient Invariant and Quasi-Invariant Structures in an Example of an Aperiodically Time Dependent Fluid Flow

Alessandro Fortunati*, Stephen Wiggins

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

Starting from the concept of invariant KAM tori for nearly-integrable Hamiltonian systems with periodic or quasi-periodic nonautonomous perturbation, the paper analyzes the "analogue" of this class of invariant objects when the dependence on time is aperiodic. The investigation is carried out in a model motivated by the problem of a traveling wave in a channel over a smooth, quasi- and asymptotically flat (from which the "transient" feature) bathymetry, representing a case in which the described structures play the role of barriers to fluid transport in phase space. The paper provides computational evidence for the existence of transient structures also for "large" values of the perturbation size, as a complement to the rigorous results already proven by the first author for real-analytic bathymetry functions.

Original languageEnglish
Article number1830015
Number of pages11
JournalInternational Journal of Bifurcation and Chaos
Volume28
Issue number5
Early online date21 May 2018
DOIs
Publication statusPublished - May 2018

Keywords

  • aperiodic KAM and Nekhoroshev theorems
  • arbitrary bathymetry
  • nearly-integrable systems
  • Shallow-water

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