Nonintegrable perturbations of two vortex dynamics

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The governing equations of motion of two point vortices in an ideal fluid in the plane has a Hamiltonian formulation that is completely integrable, so the dynamics are regular in the sense that one has quasiperiodic solutions confined to invariant two-dimensional tori accompanied by periodic orbits. Moreover, it is well known that the same is true of the dynamics of two point vortices in an ideal fluid in a standard half-plane (with a straight line boundary). It is natural to ask if this is also the case for half-planes whose boundaries are perturbations of a straight line. We prove here that there are such Hamiltonian perturbations of two vortex dynamics in the half-plane that generate chaotic - and a fortiori nonintegrable - dynamics, thereby answering an open question of rather long standing. Our proof, like most demonstrations of this kind, is based on Melnikov's method.

Original languageEnglish (US)
Title of host publicationIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium
PublisherSpringer Verlag
Pages331-340
Number of pages10
ISBN (Print)9781402067433
DOIs
StatePublished - 2008
EventIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Moscow, Russian Federation
Duration: Aug 25 2006Aug 30 2006

Publication series

NameSolid Mechanics and its Applications
Volume6
ISSN (Print)1875-3507

Other

OtherIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence
CountryRussian Federation
CityMoscow
Period8/25/068/30/06

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Acoustics and Ultrasonics
  • Mechanical Engineering

Keywords

  • Chaos
  • Hamiltonian dynamics
  • Integrability
  • Melnikov's method
  • Transverse heteroclinic orbits

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