Regularized Euler-α motion of an infinite array of vortex sheets

Russel Caflisch, F. Gargano, M. Sammartino, V. Sciacca

Research output: Contribution to journalArticle

Abstract

We consider the Euler-α regularization of the Birkhoff-Rott equation and compare its solutions with the dynamics of the non regularized vortex-sheet. For a flow induced by an infinite array of planar vortex-sheets we analyze the complex singularities of the solutions.Through the singularity tracking method we show that the regularized solution has several complex singularities that approach the real axis. We relate their presence to the formation of two high-curvature points in the vortex sheet during the roll-up phenomenon.

Original languageEnglish (US)
Pages (from-to)113-141
Number of pages29
JournalBolletino dell Unione Matematica Italiana
Volume10
Issue number1
DOIs
StatePublished - Mar 1 2017

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Vortex Sheet
Euler
Singularity
Motion
Regularization
Curvature

Keywords

  • Birkhoff-Rott equation
  • Complex singularities
  • Euler-α regularization
  • Vortex-sheet

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Regularized Euler-α motion of an infinite array of vortex sheets. / Caflisch, Russel; Gargano, F.; Sammartino, M.; Sciacca, V.

In: Bolletino dell Unione Matematica Italiana, Vol. 10, No. 1, 01.03.2017, p. 113-141.

Research output: Contribution to journalArticle

Caflisch, Russel ; Gargano, F. ; Sammartino, M. ; Sciacca, V. / Regularized Euler-α motion of an infinite array of vortex sheets. In: Bolletino dell Unione Matematica Italiana. 2017 ; Vol. 10, No. 1. pp. 113-141.
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