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

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6 Citations (Scopus)

Abstract

We consider the Euler-alpha 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
Pages (from-to)113-141
Number of pages29
JournalBOLLETTINO DELLA UNIONE MATEMATICA ITALIANA
Volume10
Publication statusPublished - 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics

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