Linear instability of symmetric logarithmic spiral vortex sheets
Abstract
We consider Alexander spirals with M≥ 3 branches, that is symmetric logarithmic spiral vortex sheets. We show that such vortex sheets are linearly unstable in the L∞ (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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