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arXiv · 2305.08764

Linear instability of symmetric logarithmic spiral vortex sheets

Tomasz Cieślak·Piotr Kokocki·Wojciech S. Ożański
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Abstract

We consider Alexander spirals with $M\geq 3$ branches, that is symmetric logarithmic spiral vortex sheets. We show that such vortex sheets are linearly unstable in the $L^\infty$ (Kelvin-Helmholtz) sense, as solutions to the Birkhoff-Rott equation. To this end we consider Fourier modes in a logarithmic variable to identify unstable solutions with polynomial growth in time.

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Tomasz Cieślak, Piotr Kokocki, Wojciech S. Ożański. 2023-05-15. Linear instability of symmetric logarithmic spiral vortex sheets. https://arxiv.org/abs/2305.08764

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