Stability of vortex lattices in rotating flows
Abstract
Vortex lattices-highly ordered arrays of vortices-are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating fluids. However, the mechanisms governing their formation, stability, and eventual breakdown remain poorly understood. We explore the dynamical stability of vortex lattices in three-dimensional rotating flows. To that end we construct controlled initial conditions consisting of vortex lattices superimposed on turbulent backgrounds. We then characterize their evolution across different Rossby numbers and domain geometries. By introducing an Ekman drag we are able to reach a steady state where vortex lattices persist with near constant amplitude up until spontaneous breakup of the lattice, or an equivalent of "melting," occurs. We examine an ensemble of runs in order to determine the mean lifetime of the lattice as a function of the system parameters. Our results reveal that the stability of the lattices is a memory-less random process whose mean life-time depends sensitively on the system parameters that if finely tuned can lead to very long lived lattice states. These metastable states exhibit statistical properties reminiscent of critical systems and can offer insight into long-lived vortex patterns observed in planetary atmospheres.
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BibTeX
@article{estrada2026stability,
title = {{Stability of vortex lattices in rotating flows}},
author = {Julián Amette Estrada and Alexandros Alexakis and Marc Brachet and Pablo Mininni},
journal = {Physical Review Fluids},
year = {2026},
month = sep,
doi = {10.1103/k8zw-s6kj},
eprint = {2510.06374},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05738441v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Stability of vortex lattices in rotating flows
AU - Julián Amette Estrada
AU - Alexandros Alexakis
AU - Marc Brachet
AU - Pablo Mininni
PY - 2026
DA - 2026/09/04
JO - Physical Review Fluids
DO - 10.1103/k8zw-s6kj
UR - https://hal.science/hal-05738441v1
AB - Vortex lattices-highly ordered arrays of vortices-are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating fluids. However, the mechanisms governing their formation, stability, and eventual breakdown remain poorly understood. We explore the dynamical stability of vortex lattices in three-dimensional rotating flows. To that end we construct controlled initial conditions consisting of vortex lattices superimposed on turbulent backgrounds. We then characterize their evolution across different Rossby numbers and domain geometries. By introducing an Ekman drag we are able to reach a steady state where vortex lattices persist with near constant amplitude up until spontaneous breakup of the lattice, or an equivalent of "melting," occurs. We examine an ensemble of runs in order to determine the mean lifetime of the lattice as a function of the system parameters. Our results reveal that the stability of the lattices is a memory-less random process whose mean life-time depends sensitively on the system parameters that if finely tuned can lead to very long lived lattice states. These metastable states exhibit statistical properties reminiscent of critical systems and can offer insight into long-lived vortex patterns observed in planetary atmospheres.
SN - 2469-990X
ER -