Network broadcast analysis and control of turbulent flows

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.

Automated summary

This study introduces a network-based modal analysis technique utilizing Katz centrality to identify key dynamical paths for amplifying perturbations on time-varying base flows, with broadcast modes revealing sensitive regions in the fluid-flow network. The application to two-dimensional decaying isotropic turbulence highlights the importance of vortex dipoles in perturbation spreading, demonstrating the effectiveness of modifying turbulent evolution through flow perturbation. This network-inspired approach presents a novel use of network analysis for guiding flow control efforts, particularly for time-varying base flows.