PreprintCC BY 4.0arXiv
A catalog of exact steady states in Kolmogorov flow
Abstract
Two-dimensional Kolmogorov flow is a common proving ground for the dynamical systems picture of turbulence. Hundreds of unstable periodic orbits have been found for this system across many Reynolds numbers and domain sizes, although the most well explored is Re=40 on a square 2π× 2π domain with a forcing wavenumber of k=4. Here I present a catalog of 8952 exact steady states of the flow in this canonical parameter regime. These solutions provide a fixed constellation informing the dynamics of both turbulence and transients.
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BibTeX
@misc{golden2026catalog,
title = {{A catalog of exact steady states in Kolmogorov flow}},
author = {Matthew Golden},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27062},
eprint = {2609.27062},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27062},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A catalog of exact steady states in Kolmogorov flow
AU - Matthew Golden
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.27062
UR - https://arxiv.org/abs/2609.27062
AB - Two-dimensional Kolmogorov flow is a common proving ground for the dynamical systems picture of turbulence. Hundreds of unstable periodic orbits have been found for this system across many Reynolds numbers and domain sizes, although the most well explored is Re=40 on a square 2π× 2π domain with a forcing wavenumber of k=4. Here I present a catalog of 8952 exact steady states of the flow in this canonical parameter regime. These solutions provide a fixed constellation informing the dynamics of both turbulence and transients.
ER -