Numerical evidence of nonuniqueness in the evolution of vortex sheets

Milton C. Lopes Filho, John Lowengrub, Helena J. Nussenzveig Lopes, Yuxi Zheng

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

We consider a special configuration of vorticity that consists of a pair of externally tangent circular vortex sheets, each having a circularly symmetric core of bounded vorticity concentric to the sheet, and each core precisely balancing the vorticity mass of the sheet. This configuration is a stationary weak solution of the 2D incompressible Euler equations. We propose to perform numerical experiments to verify that certain approximations of this flow configuration converge to a non-stationary weak solution. Preliminary simulations presented here suggest this is indeed the case. We establish a convergence theorem for the vortex blob method that applies to this problem. This theorem and the preliminary calculations we carried out support the existence of two distinct weak solutions with the same initial data.

Original languageEnglish (US)
Pages (from-to)225-237
Number of pages13
JournalMathematical Modelling and Numerical Analysis
Volume40
Issue number2
DOIs
StatePublished - Jun 29 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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