Anti-Holomorphic Modes in Vortex Lattices
arXiv:2201.05200 · doi:10.21468/SciPostPhys.14.4.080
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.
12 pages, 8 figures. v3: Final version
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