@article{9558,
  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.
},
  author       = {Yalniz, Gökhan and Hof, Björn and Budanur, Nazmi B},
  issn         = {1079-7114},
  journal      = {Physical Review Letters},
  number       = {24},
  publisher    = {American Physical Society},
  title        = {{Coarse graining the state space of a turbulent flow using periodic orbits}},
  doi          = {10.1103/PhysRevLett.126.244502},
  volume       = {126},
  year         = {2021},
}