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Network broadcast analysis and control of turbulent flows

Published online by Cambridge University Press:  08 January 2021

Chi-An Yeh Open the ORCID record for Chi-An Yeh [Opens in a new window] ,
Muralikrishnan Gopalakrishnan Meena Open the ORCID record for Muralikrishnan Gopalakrishnan Meena [Opens in a new window]  and
Kunihiko Taira Open the ORCID record for Kunihiko Taira [Opens in a new window]
Chi-An Yeh*
Affiliation:
Mechanical and Aerospace Engineering, University of California, Los Angeles, CA90095, USA
Muralikrishnan Gopalakrishnan Meena
Affiliation:
Mechanical and Aerospace Engineering, University of California, Los Angeles, CA90095, USA
Kunihiko Taira
Affiliation:
Mechanical and Aerospace Engineering, University of California, Los Angeles, CA90095, USA
*
†Email address for correspondence: cayeh@seas.ucla.edu
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Abstract

We present a network-based modal analysis technique that identifies key dynamical paths along which perturbations amplify over a time-varying base flow. This analysis is built upon the Katz centrality, which reveals the flow structures that can effectively spread perturbations over a time-evolving network of vortical interactions on the base flow. Motivated by the resolvent form of the Katz function, we take the singular value decomposition of the resulting communicability matrix, complementing the resolvent analysis for fluid flows. The right-singular vectors, referred to as the broadcast modes, give insights into the sensitive regions where introduced perturbations can be effectively spread and amplified over the entire fluid-flow network that evolves in time. We apply this analysis to a two-dimensional decaying isotropic turbulence. The broadcast mode reveals that vortex dipoles are important structures in spreading perturbations. By perturbing the flow with the principal broadcast mode, we demonstrate the utility of the insights gained from the present analysis for effectively modifying the evolution of turbulent flows. The current network-inspired work presents a novel use of network analysis to guide flow control efforts, in particular for time-varying base flows.

JFM classification

Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A15
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

‡

Present address: National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.

References

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