Orateur
Description
Reduced-order models (ROM) are of paramount importance for physical understanding, data
compression, estimation, control and optimization. Over a century ago, simple dynamical models
of coherent structures have been facilitated by stability theory (Orr-Sommerfeld equation
1907) and by vortex models (von K arm an 1911). Data-driven reduced-order modeling of coherent
structures has been pioneered by Aubry et al. (1988) with a celebrated POD model of
the turbulent boundary layer. Since then, machine learning [1] has significantly simplified and
enriched the spectrum of possibilities for data-driven ROM.
In this talk, we exemplify different ROM approaches for the fluidic pinball [2], the wake flow
behind a cluster of three parallel cylinders on an equilateral triangle pointing upstream. The
flow may be actuated by rotating cylinders. First, the transition scenario of the unforced fluidic
pinball is modeled with a five-mode mean-field Galerkin model. This model comprises
successive Hopf and pitchfork bifucations, which are typical for a number of wake flows. Second,
a cluster-based network model (CNM) [3, 4] is presented describing the fluidic pinball
wake with actuation as free input, employing thousand differently actuated pinball simulations.
CNM yields a robust dynamics from a fully automatable procedure. Finally, perspectives of
ROM for common tasks of data management are given.
[1] BRUNTON, S. L., NOACK, B. R. & KOUMOUTASKOS, P. 2020 Ann. Rev. Fluid Mech. 52:477–
508.
[2] DENG, N., NOACK, B. R., MORZY N SKI, M., & PASTUR, L. R. 2020 Low-order model for
successive bifurcations of the fluidic pinball. J. Fluid Mech. 884, A37:1–41.
[3] LI, H., FERNEX, D., SEMAAN, R., TAN, J., MORZY N SKI, M. & NOACK, B. R. 2021 Clusterbased
network model. J. Fluid Mech. 906, A21:1–41.
[4] FERNEX, D., NOACK, B. R. & SEMAAN, R. 2021 Cluster-based network model—From snapshots
to complex dynamical systems. Science Advances (online).
Bernd R. Noack 1, Nan Deng1, Daniel Fernex2
Luc Pastur3, Richard Semaan4 Marek Morzy nski5
1 Harbin Institute of Technology, Shenzhen, China,
2 EPFL, Switzerland,
3 ENSTA, Paris,
4 TU Braunschweig, Germany,
5 Poznan University of Technology, Poland
