Characterizing influential networked structures in isotropic turbulence

We characterize the complex nonlinear vortical interactions in two- and three-dimensional decaying isotropic turbulence through network-theoretic formulations and use network-based measures to identify and quantify the effects of influential structures on mixing enhancement. The web of interactions among vortical elements can be represented in a network-based framework where the vortical elements are the nodes and the vortical interactions are edges quantified by induced velocity following the Biot-Savart law. We find relationship between enstrophy and interaction strength, distribution of which gives an overall interaction behavior of the flow. Identification of vortical communities, groups of closely interacting nodes, enables the classification of shear layers and vortex core dominated structures as network connector and peripheral structures respectively. These respective elements exhibit inter-community and intra-community interactions. Furthermore, we find that perturbing the connectors and peripherals by adding and removing energy respectively can enhance mixing in both 2D and 3D decaying isotropic turbulence.