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arXiv · 2609.27062

A catalog of exact steady states in Kolmogorov flow

Matthew Golden
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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 $2π\times 2π$ 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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Matthew Golden. 2026-09-22. A catalog of exact steady states in Kolmogorov flow. https://arxiv.org/abs/2609.27062

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