Mixing layer growth response to inflow forcing with random phase shift

We study the sensitivity of the formation and the evolution of large-scale coherent structures in spatially developing plane mixing layers to uncertainties in the inflow forcing phase shifts. Instead of examining the mixing layer growth at discrete phase values, a complete response is determined by treating the phase shift as periodic and uniformly distributed random variables. The Fourier Chaos expansion (FCE) is used to decompose the stochastic solution in the abstract random space and the coefficients are determined by the discrete Fourier transformation (DFT). The statistical moments and quantiles of pertinent physical measures were determined. In the bimodal perturbation case, the vortex interactions are sensitive to only a small range of phase differences where large downstream variations in mixing layer growths are observed. In the tri-modal perturbation case, mixing layer growth is especially sensitive to the phase difference between the fundamental and the subharmonic modes immediately downstream from the inlet. Near the downstream location with subharmonic vortices roll up, an increase of the influence of the phase difference between the subharmonic modes can be observed. In both cases, the stochastic phase differences between the perturbation modes are delayed further downstream in comparison to the stochastic perturbation magnitudes. Quantiles of discrete vortex pairing events and different mixing layer length scales are also estimated.