Dynamics of (4+1)-dihedrally symmetric nearly parallel vortex filaments

Francesco Paparella, Alessandro Portaluri

Research output: Contribution to journalArticle

Abstract

We give a detailed analytical and numerical description of the global dynamics of 4+1 points interacting through the singular logarithmic potential and subject to the following symmetry constraint: at each instant 4 of them form an orbit of the Klein group D 2 of order 4. The main device in order to achieve our results is to use a McGehee-like transformation introduced in (Paparella and Portaluri in Global dynamics of the dihedral singular logarithmic potential and nearly parallel vortex filaments, 2011) for a problem analogous to the present one. After performing this transformation in order to regularize the total collision, we study the rest-points of the flow, the invariant (stable and unstable) manifolds and we derive some interesting information about the global dynamics.

Original languageEnglish (US)
Pages (from-to)349-366
Number of pages18
JournalActa Applicandae Mathematicae
Volume122
Issue number1
DOIs
StatePublished - Dec 1 2012

Fingerprint

Vortex Filament
Global Dynamics
Logarithmic Potential
Vortex flow
Stable and Unstable Manifolds
Invariant Manifolds
Instant
Orbits
Collision
Orbit
Symmetry

Keywords

  • Dihedral N-vortex filaments
  • Global dynamics
  • McGehee coordinates

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Dynamics of (4+1)-dihedrally symmetric nearly parallel vortex filaments. / Paparella, Francesco; Portaluri, Alessandro.

In: Acta Applicandae Mathematicae, Vol. 122, No. 1, 01.12.2012, p. 349-366.

Research output: Contribution to journalArticle

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