Bispectral analysis and phase coupling of triadic interactions in a turbulent boundary layer

Turbulent boundary layers are characterized by a wide range of scales from large meandering coherent structures longer than the boundary layer height to small near-wall viscous scales. Spectral energy transfer, which imposes inter-scale dynamics through the turbulent cascade, is a non-linear process based on triadic interactions. Triads are subject to a sum-zero condition of three wavenumber vectors or frequencies. The complete identification of triadic interactions is difficult to elucidate solely through the power spectrum, as it is phase blind. Wall modeled large-eddy simulations of a turbulent boundary layer are conducted within a domain sufficiently large to capture large-scale meandering features in order to quantify the magnitude and phase of triads in energy transfer. We employ bispectral analyses in both wavenumber and frequency space to identify triadic interactions across the disparate range of scales. First, we examine the wall-parallel planar wavenumber bispectrum changes with distance from the wall. Second, we use frequency-space bispectral analysis based on mode decomposition to identify coherent structures and their phase-coupling to other scales. Modal energy budgets at specific scales show how nonlinearity contributes to scale development in a turbulent boundary layer.