A large volume of experimental and numerical evidence suggests that the dynamics of turbulent flows are underpinned by “coherent structures,” which is an umbrella term for flow patterns that persist for some time. Besides their observations, the theoretical works of the past forty years have also established causal connections between the coherent structures, such as the self-sustaining cycle of streaks and vortices in shear flows. Altogether, these developments suggest that the coherent structures can be utilized for producing reduced-order models of turbulence, yet, the methodology for developing such models remains to be established. In the first part of my talk, I will introduce one approach to this problem based on the coarse-graining of the state space using periodic orbits and present the results of its application to the sinusoidally-driven flow in a triply-periodic domain [1, 2]. In the second part, I will describe the combination of symmetry-reduction and data-driven methods that enables us to extend this methodology to wall-bounded turbulence and show preliminary results for plane-Couette and Poiseuille flows [3].

References:

[1] G. Yalnız, N. B. Budanur, Inferring symbolic dynamics of chaotic flows from persistence, Chaos 30, 033109 (2020), arXiv:1910.04584.

[2] G. Yalnız, B. Hof, and N. B. Budanur, Coarse graining the state space of a turbulent flow using periodic orbits, Phys. Rev. Lett. 126, 244502 (2021) arXiv:2007.02584.

[3] E. Marensi, G. Yalnız, B. Hof, and N. B. Budanur, Symmetry-reduced Dynamic Mode Decomposition of Near-wall Turbulence, arXiv:2101.07516.