Singular behavior of a vortex layer in the zero thickness limit

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Abstract

The aim of this paper is to study the Euler dynamics of a 2D periodic layer of non uniform vorticity. We consider the zero thickness limit and we compare the Euler solution with the vortex sheet evolution predicted by the Birkhoff-Rott equation. The well known process of singularity formation in shape of the vortex sheet correlates with the appearance of several complex singularities in the Euler solution with the vortex layer datum. These singularities approach the real axis and are responsible for the roll-up process in the layer motion.
Original languageEnglish
Pages (from-to)553-572
Number of pages20
JournalATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI
Volume28
Publication statusPublished - 2017

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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