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Variety of unsymmetric multibranched logarithmic vortex spirals

Published online by Cambridge University Press:  22 December 2017

V. ELLING  and
M. V. GNANN
V. ELLING
Affiliation:
Department of Mathematics, Academia Sinica, 6F Astronomy-Mathematics Bldg., No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan email: velling@math.sinica.edu.tw
M. V. GNANN
Affiliation:
Center for Mathematics, Technical University of Munich, Boltzmannstr. 3, 85748 Garching near Munich, Germany email: gnann@ma.tum.de
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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.

Keywords

76B4735Q3135C06
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 1 , February 2019 , pp. 23 - 38
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

The authors' research was partially supported by the National Science Foundation under Grant NSF DMS-1054115 and by Taiwan MOST grant 105-2115-M-001-007-MY3.

References

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