A nonlinear approximation for vortex sheet evolution and singularity formation

Russel E. Caflisch, Stephen Semmes

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - Mar 1990

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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