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Applied Koopmanistic interpretation of subcritical prism wake physics using the dynamic mode decomposition

  • Cruz Y. Li (Department of Civil Engineering, Chongqing University) ;
  • Xisheng Lin (Department of Civil and Environmental Engineering, the Hong Kong University of Science and Technology) ;
  • Gang Hu (School of Civil and Environmental Engineering, Harbin Institute of Technology) ;
  • Lei Zhou (Department of Civil and Environmental Engineering, the Hong Kong University of Science and Technology) ;
  • Tim K.T. Tse (Department of Civil Engineering, Chongqing University) ;
  • Yunfei Fu (Department of Civil and Environmental Engineering, the Hong Kong University of Science and Technology)
  • Received : 2022.08.18
  • Accepted : 2023.04.20
  • Published : 2023.09.25
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Abstract

This work investigates the subcritical free-shear prism wake at Re=22,000 by the Koopman analysis using the Dynamic Mode Decomposition (DMD) algorithm. The Koopman model linearized nonlinearities in the stochastic, homogeneous anisotropic turbulent wake, generating temporally orthogonal eigen tuples that carry meaningful, coherent structures. Phenomenological analysis of dominant modes revealed their physical interpretations: Mode 1 renders the mean-field dynamics, Modes 2 describes the roll-up of the Strouhal vortex, Mode 3 describes the Bloor-Gerrard vortex resulting from the Kelvin-Helmholtz instability inside shear layers, its superposition onto the Strouhal vortex, and the concurrent flow entrainment, Modes 6 and 10 describe the low-frequency shedding of turbulent separation bubbles (TSBs) and turbulence production, respectively, which contribute to the beating phenomenon in the lift time history and the flapping motion of shear layers, Modes 4, 5, 7, 8, and 9 are the relatively trivial harmonic excitations. This work demonstrates the Koopman analysis' ability to provide insights into free-shear flows. Its success in subcritical turbulence also serves as an excellent reference for applications in other nonlinear, stochastic systems.

Keywords

Acknowledgement

We give a special thanks to the IT Office of the Department of Civil and Environmental Engineering at the Hong Kong University of Science and Technology. Its support for installing, testing, and maintaining our high-performance servers is indispensable for the current project.

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