Anti-Holomorphic Modes in Vortex Lattices
Fluid Dynamics
2023-04-26 v3 Quantum Gases
Soft Condensed Matter
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2201.05200,
title = {Anti-Holomorphic Modes in Vortex Lattices},
author = {Brook J Hocking and Thomas Machon},
journal= {arXiv preprint arXiv:2201.05200},
year = {2023}
}
Comments
12 pages, 8 figures. v3: Final version