Bispectral mode and scale analysis of wind turbine wake meandering

Large atmospheric boundary layer fluctuations and smaller turbine-scale vorticity dynamics are separately hypothesized to initiate the wind turbine wake meandering phenomenon, a coherent, dynamic, turbine-scale oscillation of the far wake. The effects of upwind scales on wake meandering are assessed by considering kinetic energy transfer between the dominant spatio-temporal scales. Triadic interactions, which are the mechanism of energy transfers between scales, manifests as a triple of wavenumbers or frequencies. The bispectrum is a function of two frequencies, which correlates the two frequencies to their sum, and identifies triads. A large-eddy simulation of a utility-scale wind turbine are used to acquire instantaneous velocity snapshots upwind and downwind of the turbine. A precursory simulation is employed to provide an inflow that contains a broad range of length-scales up to over an order of magnitude greater than the turbine diameter. Prominent upwind and downwind coherent structures, including upwind boundary layer scales, turbine rotor scales, and wake meandering are identified through two methods: bispectral mode decomposition and an energy transfer method based on triple decomposition and dynamic mode decomposition. The bispectrum from both methods is used to characterize the triadic interactions.