Fluid and Biodynamics Seminar: Investigating triadic interactions: from a perturbed canonical boundary layer to heart murmurs

Through understanding the scales and frequencies that dominate a turbulent flow, we can re-veal the physics and nature of the system being investigated. From studying how external per-turbations can decrease skin friction to how defects and failures can be diagnosed through changes in a signal, the interactions of frequencies are used in making these connections. In a turbulent flow, perturbing appropriate frequencies and wavenumbers excited triadic interactions that lead to increases or reductions in statistics such as the wall shear, variance, skewness, and other Reynolds stresses. A study is performed on the nonlinear interactions due to dynamic wall perturbations in a turbulent boundary layer using the bispectrum, which is the Fourier trans-form of the third order correlation of a signal. This third-order measure unveils the triadic inter-actions 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 provid-ing insight into what scales should be excited in a particular experimental setup for maximizing, or minimizing, the impact on the flow statistics. This framework is then used to investigate a model heart murmur to determine diagnostic markers based on the frequency interactions in the acoustic spectrum.