On the motion of two-dimensional vortices with mass
type: Item
instance of: scholarly article
title: On the motion of two-dimensional vortices with mass
zbMATH Open document ID: 0808.76015
DOI: 10.1007/BF02430639
author: V. Pereyra
published in: Journal of Nonlinear Science
publication date: 1995-03-21T00:00:00Z
review text: The Helmholtz-Kirchhoff ODEs governing the planar motion of \(N\) point vortices in an ideal, incompressible fluid are extended to the case where the fluid has impurities. In this case the resulting ODEs have an additional inertia-type term, so the point vortices are termed massive. Using the symmetries, we reduce the four degrees of freedom system of two ``massive'' vortices to two degrees of freedom system. We exhibit an integrable case and a nonintegrable one, according to choices of parameters. Finally, we discuss the behavior of solutions as the masses of the vortices tend to zero, using for initial conditions a point of the trajectory of the Helmholtz-Kirchhoff equations.
Mathematics Subject Classification ID: 76B47
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 679531
zbMATH Keywords: singular perturbations
zbMATH Keywords: transversal homoclinic orbits
zbMATH Keywords: nonintegrable case
zbMATH Keywords: planar motion
zbMATH Keywords: impurities
zbMATH Keywords: inertia-type term
zbMATH Keywords: symmetries
zbMATH Keywords: integrable case
zbMATH Keywords: Helmholtz-Kirchhoff equations
Wikidata QID: Q121450441
Wikidata QID: Q121450446
Wikidata QID: Q121450479
describes a project that uses: IMSL Numerical Libraries
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02430639
OpenAlex ID: W2061228257
description: scientific article; zbMATH DE number 679531