Landau damping and mode-selective instability of a vortex gas
Abstract
We show that a collisionless point-vortex gas behaves as a genuine Vlasov system. Starting from the non-canonical Hamiltonian structure of point-vortex dynamics, we derive a reduced Klimontovich equation and the corresponding Vlasov description directly on the physical plane, without introducing auxiliary momentum variables. The theory predicts a rich spectrum of collective phenomena, including vortex Rossby-like waves, global oscillations, resonant critical layers, and a dielectric response operator analogous to that of plasmas and self-gravitating systems. For smooth vortex distributions, differential rotation gives rise to a vortex analogue of Landau damping, whereby collective modes transfer energy and angular momentum to resonant vortex annuli in the absence of collisions or dissipation. Remarkably, differential rotation acts as a stringent mode-selection mechanism: for a Gaussian vortex cloud, only a single quadrupolar quasi-mode survives, while all higher multipoles are destroyed by phase mixing. We further predict a vortex counterpart of the beam--plasma instability, in which a thin vortex ring orbiting an Onsager patch selectively excites Kelvin modes with an azimuthal symmetry controlled by the ring population. These results establish kinetic theory as a natural framework for collective vortex dynamics and suggest new mechanisms for vortex transport, vortex avalanches, and rotational glitches in neutron-star superfluids.
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BibTeX
@misc{tercas2026landau,
title = {{Landau damping and mode-selective instability of a vortex gas}},
author = {H. Terças and J. L. Figueiredo and J. T and Mendonça},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04841},
eprint = {2610.04841},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04841},
}
RIS
TY - UNPB
TI - Landau damping and mode-selective instability of a vortex gas
AU - H. Terças
AU - J. L. Figueiredo
AU - J. T
AU - Mendonça
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04841
UR - https://arxiv.org/abs/2610.04841
AB - We show that a collisionless point-vortex gas behaves as a genuine Vlasov system. Starting from the non-canonical Hamiltonian structure of point-vortex dynamics, we derive a reduced Klimontovich equation and the corresponding Vlasov description directly on the physical plane, without introducing auxiliary momentum variables. The theory predicts a rich spectrum of collective phenomena, including vortex Rossby-like waves, global oscillations, resonant critical layers, and a dielectric response operator analogous to that of plasmas and self-gravitating systems. For smooth vortex distributions, differential rotation gives rise to a vortex analogue of Landau damping, whereby collective modes transfer energy and angular momentum to resonant vortex annuli in the absence of collisions or dissipation. Remarkably, differential rotation acts as a stringent mode-selection mechanism: for a Gaussian vortex cloud, only a single quadrupolar quasi-mode survives, while all higher multipoles are destroyed by phase mixing. We further predict a vortex counterpart of the beam--plasma instability, in which a thin vortex ring orbiting an Onsager patch selectively excites Kelvin modes with an azimuthal symmetry controlled by the ring population. These results establish kinetic theory as a natural framework for collective vortex dynamics and suggest new mechanisms for vortex transport, vortex avalanches, and rotational glitches in neutron-star superfluids.
ER -