Variety of unsymmetric multibranched logarithmic vortex spirals

Manuel Gnann, Volker Elling

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

Building on work of Prandtl and Alexander, we study logarithmic vortex spiral solutions of the two-dimensional incompressible Euler equations. We consider multi-branched spirals that are not symmetric, including mixtures of sheets and continuum vorticity. We find that non-trivial solutions allow only sheets, that there is a large variety of such solutions, but that only the Alexander spirals with three or more symmetric branches appear to yield convergent Biot–Savart integral.
Original languageEnglish
Pages (from-to)23
Number of pages38
JournalEuropean Journal of Applied Mathematics
Volume30
Issue number1
Publication statusPublished - Feb 2019
Externally publishedYes

Keywords

  • 76B47
  • 35Q31
  • 35C06

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