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

Linear instability of symmetric logarithmic spiral vortex sheets