Network broadcast mode analysis and control of turbulent flows
Published 2020-06-29Version 1
We present a network-based modal analysis that identifies the key dynamical paths along which perturbations amplify in an isotropic turbulent flow. This analysis is built upon the Katz centrality, which reveals the flow structures that can effectively spread perturbations over the time-evolving network of vortical elements that constitute the turbulent flow field. Motivated by the resolvent form of the Katz function, we take the singular value decomposition of the resulting communicability matrix, complementing resolvent analysis. The right-singular vector, referred to as the broadcast mode, gives insights into the sensitive regions where introduced perturbations can be effectively spread over the entire fluid-flow network as it evolves over time. The broadcast mode reveals that vortex dipoles are the important structures in spreading perturbations. By perturbing the flow with the broadcast mode, we demonstrate its capability to effectively modify 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 turbulent base flows.