A nonlinear approximation for vortex sheet evolution and singularity formation

Russel Caflisch, Stephen Semmes

Research output: Contribution to journalArticle

Abstract

The evolution of a vortex sheet in two-dimensional, incompressible, inviscid flow is governed by the integro-differential equation of Birkhoff-Rott. We derive a simple approximation for vortex sheet evolution, consisting of a system of four first-order differential equations. This approximate system has the advantage of involving only local operators. The errors in the approximation are shown to be relatively small even if the sheet has infinite curvature at a point. For the approximate equations, exact similarity solutions exhibiting singularity formation are constructed.

Original languageEnglish (US)
Pages (from-to)197-207
Number of pages11
JournalPhysica D: Nonlinear Phenomena
Volume41
Issue number2
DOIs
StatePublished - 1990

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vortex sheets
differential equations
inviscid flow
approximation
curvature
operators

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

Cite this

A nonlinear approximation for vortex sheet evolution and singularity formation. / Caflisch, Russel; Semmes, Stephen.

In: Physica D: Nonlinear Phenomena, Vol. 41, No. 2, 1990, p. 197-207.

Research output: Contribution to journalArticle

Caflisch, Russel ; Semmes, Stephen. / A nonlinear approximation for vortex sheet evolution and singularity formation. In: Physica D: Nonlinear Phenomena. 1990 ; Vol. 41, No. 2. pp. 197-207.
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