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. Solu...
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| Format: | Article |
| Language: | English |
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SciPost
2023-04-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.14.4.080 |
| Summary: | 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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| ISSN: | 2542-4653 |