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

    Research areas

  • 76B47, 35Q31, 35C06

ID: 68495500