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We show that turbulent dynamics that arise in simulations of thethree-dimensional Navier--Stokes equations in a triply-periodic domain undersinusoidal forcing can be described as transient visits to the neighborhoods ofunstable time-periodic solutions. Based on this description, we reduce theoriginal system with more than $10^5$ degrees of freedom to a 17-node Markovchain where each node corresponds to the neighborhood of a periodic orbit. Themodel accurately reproduces long-term averages of the system's observables asweighted sums over the periodic orbits.

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