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Self-Similar 2d Euler Solutions with Mixed-Sign Vorticity

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Abstract

We construct a class of self-similar 2d incompressible Euler solutions that have initial vorticity of mixed sign. The boundaries between regions of positive and negative vorticity form algebraic spirals, similar to the Kaden spiral and as opposed to Prandtl’s logarithmic vortex spirals. Also unlike the Prandtl case, spirals are not initially present.

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  1. University of Michigan, Ann Arbor, USA

    Volker Elling

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  1. Volker Elling
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Correspondence to Volker Elling.

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Communicated by C. Mouhot

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Elling, V. Self-Similar 2d Euler Solutions with Mixed-Sign Vorticity. Commun. Math. Phys. 348, 27–68 (2016). https://doi.org/10.1007/s00220-016-2755-z

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  • DOI: https://doi.org/10.1007/s00220-016-2755-z

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