Investigating triadic interactions in an externally perturbed boundary layer

The control of turbulent flows through external active excitation has received significant attention. By perturbing appropriate frequencies and wavenumbers within the flow domain, the triadic interactions can lead to increases or reductions in statistics such as the wall shear, variance, skewness, and other Reynolds stresses. This study investigates nonlinear interactions due to dynamic wall perturbations in a turbulent boundary layer using the bispectrum, which is the Fourier transform of the third order correlation of a signal. This third-order measure unveils the triadic interactions in the velocity, including the intensity of coupling between frequencies. The phase of the bispectrum reveals whether triads have forward or reverse cascades, elucidating how forcing can add or disrupt the energy at targeted frequencies. A summation over frequency bins shows the scale-dependent contributions to the velocity skewness and derivative skewness, revealing the scales that are most active in energy transfer. All these measures are performed without any need for artificial filtering or arbitrary scale decomposition, demonstrating the usefulness of the bispectrum in assessing the impact of external perturbations on turbulent flows and providing insight into what scales should be excited in a particular experimental setup for maximizing, or minimizing, the impact on the flow statistics.