Papers › Coarse graining the state space of a turbulent flow using periodic orbits
Coarse graining the state space of a turbulent flow using periodic orbits
Gökhan Yalnız, Björn Hof, Nazmi Burak Budanur
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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 10⁵ 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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