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On the motion of a vortex ring with a sharply concentrated vorticity
Author(s) -
Benedetto D.,
Caglioti E.,
Marchioro C.
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(20000125)23:2<147::aid-mma108>3.0.co;2-j
Subject(s) - vorticity , annulus (botany) , mathematics , vorticity equation , vortex , burgers vortex , limit (mathematics) , constant (computer programming) , compressibility , motion (physics) , classical mechanics , euler equations , mathematical analysis , vortex ring , mathematical physics , mechanics , physics , botany , computer science , biology , programming language
We study an incompressible non‐viscous fluid with axial symmetry without swirl, in the case when the vorticity is supported in an annulus. It is well known that there exist particular initial data for which the Euler evolution reduces to a translation with a constant speed. In this paper we prove a similar property for any initial condition in the limit situation in which the initial vorticity is sharply concentrated. Copyright © 2000 John Wiley & Sons, Ltd.