Data-driven dimensionality reduction methods such as proper orthogonal decomposition and dynamic mode decomposition have proven to be useful for exploring complex phenomena within fluid dynamics and beyond. A well-known challenge for these techniques is posed by the continuous symmetries, e.g. translations and rotations, of the system under consideration, as drifts in the data dominate the modal expansions without providing an insight into the dynamics of the problem. In the present study, we address this issue for fluid flows in rectangular channels by formulating a continuous symmetry reduction method that eliminates the translations in the streamwise and spanwise directions simultaneously. We demonstrate our method by computing the symmetry-reduced dynamic mode decomposition (SRDMD) of sliding windows of data obtained from the transitional plane-Couette and turbulent plane-Poiseuille flow simulations. In the former setting, SRDMD captures the dynamics in the vicinity of the invariant solutions with translation symmetries, i.e. travelling waves and relative periodic orbits, whereas in the latter, our calculations reveal episodes of turbulent time evolution that can be approximated by a low-dimensional linear expansion.
Journal of Fluid Mechanics
E.M. acknowledges funding from the ISTplus fellowship programme. G.Y. and B.H. acknowledge a grant from the Simons Foundation (662960, BH).
Marensi E, Yalniz G, Hof B, Budanur NB. Symmetry-reduced dynamic mode decomposition of near-wall turbulence. Journal of Fluid Mechanics. 2023;954. doi:10.1017/jfm.2022.1001
Marensi, E., Yalniz, G., Hof, B., & Budanur, N. B. (2023). Symmetry-reduced dynamic mode decomposition of near-wall turbulence. Journal of Fluid Mechanics. Cambridge University Press. https://doi.org/10.1017/jfm.2022.1001
Marensi, Elena, Gökhan Yalniz, Björn Hof, and Nazmi B Budanur. “Symmetry-Reduced Dynamic Mode Decomposition of near-Wall Turbulence.” Journal of Fluid Mechanics. Cambridge University Press, 2023. https://doi.org/10.1017/jfm.2022.1001.
E. Marensi, G. Yalniz, B. Hof, and N. B. Budanur, “Symmetry-reduced dynamic mode decomposition of near-wall turbulence,” Journal of Fluid Mechanics, vol. 954. Cambridge University Press, 2023.
Marensi E, Yalniz G, Hof B, Budanur NB. 2023. Symmetry-reduced dynamic mode decomposition of near-wall turbulence. Journal of Fluid Mechanics. 954, A10.
Marensi, Elena, et al. “Symmetry-Reduced Dynamic Mode Decomposition of near-Wall Turbulence.” Journal of Fluid Mechanics, vol. 954, A10, Cambridge University Press, 2023, doi:10.1017/jfm.2022.1001.
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