Quantification of Scale Interaction of a Tip Vortex via Network-based Bispectral Analysis

Rotor blades induced tip vortices undergo breakdown as energy is transferred across scales, predominantly from large vortical structures to small scales. These inter-scale dynamics are restricted by triadic interactions, where nonlinear energy exchange occurs through three wavenumber vectors or frequencies. In this work, we employ a network-based framework to quantify triads and scale connections in the wake of a stationary rotor blade. Large-eddy simulations with the curvilinear immersed boundary method are conducted over a range of Reynolds number and uniform upwind flow to assess the wake dynamics of blade-induced flow features. Bispectral analysis is used to quantify phase-coupled interactions between frequency modes, which are then mapped onto two weighted, directed networks. The first network identifies the donor scales interacting with the catalyst scale, while the second network maps the donor to recipient scales. Nodes represent spectral modes, while edges indicate the magnitude of coherent kinetic energy. Through network metrics, in particular in-degree and out-degree centrality, dominant triads and pathways are identified. The networks identify organized and persistent energy triad connectivity. This bispectral network framework offers a scalable, interpretable tool for analyzing multiscale energy dynamics in vortex-dominated flows.