Identification of triadic phase coupling in wall-bounded turbulence using the bispectrum
The direction and magnitude of energy transfer between turbulence scale brought about by external forcing on a turbulent boundary layer are uncovered through the bispectrum, bicoherence, and biphase. The bispectrum is a third-order, complex-valued spectrum of the streamwise velocity that preserves the phase information between triadically consistent scales. Normalized bispectrum is the bicoherence, a measure of the relative amount of energy at a higher frequency that results from quadratic phase coupling of two lower frequencies. The phase of the bispectrum, the biphase, measures the phase lag between the high frequency and two lower frequencies that add to it, unveiling whether a triadic interaction produces a forward or reverse cascade of energy. Summing the bispectrum over triadically consistent frequencies allows a spectral decomposition of the velocity skewness and asymmetry, unveiling the triadically active scales in the energy transfer processes. An average sense of energy transfer is inferred from the phase of this skewness spectrum, which shows that scales smaller than the boundary layer thickness contribute to a forward cascade on average, while those larger than the boundary layer thickness have a mix of forward and reverse events. These measures show that the forced scales in the perturbed boundary layer have a mixture of forward and reverse energy transfer processes for different sets of triadic scales and wall-normal locations, providing a method of quantifying the effects of external perturbations on turbulent flows without any need for artificial filtering.