Network-theoretic modeling approach of triadic interactions and energy transfer in an isolated trailing vortex

Vortex-dominated flows are often characterized by strong compact vorticity and instabilities that lead to vortex breakdown. The process of breaking down vortices involves the transfer of kinetic energy from some spatio-temporal scales to new emergent scales. Triadic interactions are the fundamental mechanisms of energy transfer based on the quadratic nonlinearity of the Navier-Stokes equations. Triads are triplets of wavenumber or frequency scales that follow the sum-zero condition. In this work, triadic interaction mechanisms in the evolution and stability of isolated trailing vortices are elucidated using a novel approach based on network theory. Direct numerical simulation using a vorticity-velocity formulation are carried out for two isolated trailing vortex cases. Instantaneous velocity snapshot are used with a scale-specific energy transfer method to identify scales in the flow. Dominant triads are mapped from the bispectrum to two adjacency matrices and construct to inter-scale networks, directed networks that show pathways of interaction and energy transfer between scales. The first network defines the two scales that interact with each other, and the second maps one of the scales to the third resultant scale. In-degree centrality is employed to measure the importance of nodes, scales, in the network.