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Anti-Holomorphic Modes in Vortex Lattices. (arXiv:2201.05200v1 [physics.flu-dyn]) http://arxiv.org/abs/2201.05200

Anti-Holomorphic Modes in Vortex Lattices

A continuum theory of linearized Helmholtz-Kirchoff point vortex dynamics about a steadily rotating lattice state is developed by two separate methods: firstly by a direct procedure, secondly by taking the long-wavelength limit of Tkachenko's exact solution for a triangular vortex lattice. Solutions to the continuum theory are found, described by arbitrary anti-holomorphic functions, and give power-law localized edge modes. Numerical results for finite lattices show excellent agreement to the theory.

arxiv.org
January 17, 2022 at 3:10 AM · · feed2toot · 0 · 0 · 0
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