Variety of unsymmetric multibranched logarithmic vortex spirals

Journal article (2019)

Authors

M.V. Gnann Technische Universität München
Volker Elling Academia Sinica
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External organisation
76B47 35Q31 35C06
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Published Date

2019-2

Language

English

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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.