Complex network analysis of unsteady fluid flows

Abstract eng:
Unsteady fluid flows have rich dynamics generated from the nonlinear interactions that take place over a broad range of spatial and temporal scales. We can view these interactions to be present between vortical elements in physical space or between modal structures in wave space. To characterize these interactions, the use of network analysis that combines graph theory, operator theory, and dynamical systems theory is considered in our work. We show that network theory is able to capture the important vortical or modal interactions present in the flow field to provide physical insights beyond those from conventional analyses. The current approach enables the identification of key interactions and the examination of the resilience of the global interaction network to external disturbances. Moreover, we can derive the sparsified dynamics models that preserve conservation properties, using concepts from graph theory. Applications of network-based analysis to vortex dynamics, turbulence, and separated flows are presented.

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