Title: Network Structure of Two-Dimensional Decaying Isotropic Turbulence,
Abstract: The present paper reports on our effort to characterize vortical interactions
in complex fluid flows through the use of network analysis. In particular, we
examine the vortex interactions in two-dimensional decaying isotropic
turbulence and find that the vortical interaction network can be characterized
by a weighted scale-free network. It is found that the turbulent flow network
retains its scale-free behavior until the characteristic value of circulation
reaches a critical value. Furthermore, we show that the two-dimensional
turbulence network is resilient against random perturbations but can be greatly
influenced when forcing is focused towards the vortical structures that are
categorized as network hubs. These findings can serve as a network-analytic
foundation to examine complex geophysical and thin-film flows and take
advantage of the rapidly growing field of network theory, which complements
ongoing turbulence research based on vortex dynamics, hydrodynamic stability,
and statistics. While additional work is essential to extend the mathematical
tools from network analysis to extract deeper physical insights of turbulence,
an understanding of turbulence based on the interaction-based network-theoretic
framework presents a promising alternative in turbulence modeling and control
efforts.