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arXiv · 2201.05200

Anti-Holomorphic Modes in Vortex Lattices

Brook J Hocking·Thomas Machon
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Abstract

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.

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Brook J Hocking, Thomas Machon. 2022-01-13. Anti-Holomorphic Modes in Vortex Lattices. https://doi.org/10.21468/scipostphys.14.4.080

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