Work

A catalog of exact steady states in Kolmogorov flow

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.27062

Author: Golden, Matthew

Institutions: Georgia Institute of Technology, Los Alamos National Laboratory

Language: English

Topic: Fluid Dynamics and Turbulent Flows

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Institute for Pure and Applied Mathematics, Institute for Pure and Applied Mathematics

OpenAlex ID: W7214237014

Cites: 3

Cited by:

Related to: 10