  We introduce a network (graph) theoretic community-based framework to extract
vortical structures that serve the role of connectors for the vortical
interactions in two- and three-dimensional isotropic turbulence. The present
framework represents the vortical interactions on a network, where the vortical
elements are viewed as the nodes and the vortical interactions are regarded as
edges weighted by induced velocity. We identify closely interacting vortical
elements as vortical network communities through community detection
algorithms. We show that the inter- and intra-community interactions can be
used to decompose the governing equation for the evolution of network nodes.
These community-based interactions are used to identify the communities which
have the strongest and weakest interactions amongst them. These vortical
communities are referred to as connector and peripheral communities,
respectively. We demonstrate the influence of the network-based structures to
modify the dynamics of a collection of discrete point vortices. Taking
advantage of the strong inter-community interactions, connector community can
significantly modify the collective dynamics of vortices through the
application of multiple impulse perturbations. We then apply the
community-based framework to extract influential structures in isotropic
turbulence. The connector and peripheral communities extracted from turbulent
flows resemble shear-layer and vortex-core like structures, respectively. The
influence of the connector structures on the flow field and their neighboring
vortical structures is analyzed by adding impulse perturbations to the
connectors in direct numerical simulations. The findings are compared with the
cases of perturbing the strongest vortex tube and shear-layer regions. We find
that perturbing the connector structures enhances local turbulent mixing beyond
what are achieved by the other cases.
