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 |
| _version_ | 1797840179086491648 |
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| author | Brook J. Hocking, Thomas Machon |
| author_facet | Brook J. Hocking, Thomas Machon |
| author_sort | Brook J. Hocking, Thomas Machon |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T16:10:34Z |
| format | Article |
| id | doaj.art-f6ad7cedb62d4fcd90cc0dc5a30769ed |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-09T16:10:34Z |
| publishDate | 2023-04-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-f6ad7cedb62d4fcd90cc0dc5a30769ed2023-04-24T14:03:46ZengSciPostSciPost Physics2542-46532023-04-0114408010.21468/SciPostPhys.14.4.080Anti-holomorphic modes in vortex latticesBrook J. Hocking, Thomas MachonA 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.https://scipost.org/SciPostPhys.14.4.080 |
| spellingShingle | Brook J. Hocking, Thomas Machon Anti-holomorphic modes in vortex lattices SciPost Physics |
| title | Anti-holomorphic modes in vortex lattices |
| title_full | Anti-holomorphic modes in vortex lattices |
| title_fullStr | Anti-holomorphic modes in vortex lattices |
| title_full_unstemmed | Anti-holomorphic modes in vortex lattices |
| title_short | Anti-holomorphic modes in vortex lattices |
| title_sort | anti holomorphic modes in vortex lattices |
| url | https://scipost.org/SciPostPhys.14.4.080 |
| work_keys_str_mv | AT brookjhockingthomasmachon antiholomorphicmodesinvortexlattices |