Sensitivity of two-dimensional spatially developing mixing layers with respect to uncertain inflow conditions

The fidelity of numerical simulations of transport phenomena is often compromised by the difficulty in modeling the inherent experimental uncertainties. In this study, we examine the sensitivity of direct numerical simulations of two-dimensional spatially developing plane mixing layers to uncertainties in the inflow boundary conditions. In particular, we treat the magnitudes of discrete forcing modes (bimodal or trimodal) at the inflow as random variables. By applying a stochastic collocation method based on the generalized polynomial chaos, we determine the statistical moments and perform a sensitivity analysis of relevant time-averaged flow quantities with respect to the random inputs. In the bimodal perturbation case, we notice that the solutions are more sensitive to the changes in the subharmonic than the fundamental mode. We observe large spreads in the PDF contours of momentum and vorticity thicknesses and the most probable solution is distinctly different from the deterministic ones. In the trimodal perturbation case, the PDFs show large solution variations in momentum and vorticity thicknesses and the locations of the vortex interactions can be clearly related to the downstream evolutions of the most probable solutions. In both cases, the solution sensitivity to each perturbation mode is localized near the shear layer roll-up region associated with the respective modal frequency.