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arXiv · 2007.02584

Coarse graining the state space of a turbulent flow using periodic orbits

Gökhan Yalnız·Björn Hof·Nazmi Burak Budanur
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Abstract

We show that turbulent dynamics that arise in simulations of the three-dimensional Navier--Stokes equations in a triply-periodic domain under sinusoidal forcing can be described as transient visits to the neighborhoods of unstable time-periodic solutions. Based on this description, we reduce the original system with more than $10^5$ degrees of freedom to a 17-node Markov chain where each node corresponds to the neighborhood of a periodic orbit. The model accurately reproduces long-term averages of the system's observables as weighted sums over the periodic orbits.

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Gökhan Yalnız, Björn Hof, Nazmi Burak Budanur. 2021-05-11. Coarse graining the state space of a turbulent flow using periodic orbits. https://doi.org/10.1103/physrevlett.126.244502

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