SciPost Submission Page
Anti-Holomorphic Modes in Vortex Lattices
by Brook J Hocking, Thomas Machon
This Submission thread is now published as
Submission summary
| Submission information |
| Preprint Link: |
scipost_202207_00001v2
(pdf)
|
| Date accepted: |
2023-01-10 |
| Date submitted: |
2022-11-20 16:57 |
| Submitted by: |
Machon, Thomas |
| Submitted to: |
SciPost Physics |
| Ontological classification |
| Academic field: |
Physics |
| Specialties: |
- Condensed Matter Physics - Theory
- Fluid Dynamics
- Mathematical Physics
|
| Approaches: |
Theoretical, Computational |
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.
