The linear-time-invariance notion of the Koopman analysis. Part 2. Dynamic Koopman modes, physics interpretations and phenomenological analysis of the prism wake

Cruz Y. Li, Zengshun Chen, Tim K.T. Tse, Asiri Umenga Weerasuriya, Xuelin Zhang, Yunfei Fu, Xisheng Lin

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

This serial work presents a linear-time-invariance (LTI) notion to the Koopman analysis, finding consistent and physically meaningful Koopman modes and addressing a long-standing problem of fluid mechanics: deterministically relating the fluid excitations and corresponding structure reactions. Part 1 (Li et al., Phys. Fluids, vol. 34, no. 12, p. 125136) developed the Koopman-LTI architecture and applied it to a pedagogical prism wake. By a systematic analytical procedure, the Koopman-LTI generated sampling-independent linear models that captured all the recurring dynamics embedded in the input data, finding six corresponding, orthogonal, and in-synch fluid-structure mechanisms. This Part 2 analyses the six modal duplets to underpin their physical implications, providing a phenomenological analysis of the subcritical prism wake. Visualizing the newly proposed dynamic Koopman modes, results show that two mechanisms at St1 = 0.1242 and St5 = 0.0497 describe shear layer dynamics, the associated Bérnard-Kármán shedding and turbulence production, which together overwhelm the upstream and crosswind walls by instigating a reattachment-type of reaction. The on-wind walls' dynamical similarity renders them a spectrally unified fluid-structure interface. Another four harmonic counterparts, namely the subharmonic at St7 = 0.0683, the second harmonic at St3 = 0.2422, and two ultra-harmonics at St7 = 0.1739 and St13 = 0.1935, govern the downstream wall. Finally, this work discovered the vortex breathing phenomenon, describing the constant energy exchange in the wake's circulation-entrainment-deposition processes. With the Koopman-LTI, one may pinpoint the exact excitations responsible for a specific structure reaction, benefiting future investigations into fluid-structure interactions and nonlinear, stochastic systems.

Original languageEnglish
Article numberA15
JournalJournal of Fluid Mechanics
Volume959
DOIs
Publication statusPublished - 25 Mar 2023

Keywords

  • flow-structure interactions
  • low-dimensional models
  • wakes

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