Quantification of the effects of uncertainties in turbulent flows through generalized Polynomial Chaos

Statistical methodologies based on surrogate-models have proved to be an efficient approach to quantify the physical properties of turbulent flows. The underlying idea is to parametrize the space of possible solutions via a computationally inexpensive approximation model, which is then used to generate samples for the statistical tool at hand. In the following homogeneous isotropic turbulence (HIT) decay and Large-eddy simulation (LES) subgrid-scale modeling are considered as stochastic processes and their sensitivity to uncertainties in the energy spectrum shape is investigated by a surrogate-model approach based on the generalized Polynomial Chaos (gPC) approximation. The initial spectrum shape at large scales drives the long-time evolution of the physical quantities in HIT: this sensitivity is recovered even at high Reynolds number. In particular, a universal asymptotic behavior in which kinetic energy decays as t^-1 is not observed. The statistical average of the Smagorinsky subgrid model constant is close to the asymptotic Lilly-Smagorinsky value if the LES filter cut is applied in the inertial range at high Reynolds numbers, while a significant variance is recovered if the cut if performed in the dissipation range or if moderate Reynolds number are considered.