Network broadcast analysis and control of turbulent flows

TL;DR

This paper introduces a network-based modal analysis method using Katz centrality to identify key flow structures that amplify perturbations in turbulent flows, aiding flow control strategies.

Contribution

It develops a novel network analysis approach combining Katz centrality and SVD to analyze and control time-varying turbulent flows.

Findings

Vortex dipoles are key in spreading perturbations.

Perturbing with broadcast modes effectively modifies turbulence evolution.

Network analysis provides new insights for flow control.

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 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 base flows.