Sensitivity of the two-dimensional shearless mixing layer to the initial turbulent kinetic energy and integral length scale.

Abstract

The shearless mixing layer is generated from the interaction of two homogeneous isotropic turbulence (HIT) fields with different integral scales ℓ_{1} and ℓ_{2} and different turbulent kinetic energies E_{1} and E_{2}. In this study, the sensitivity of temporal evolutions of two-dimensional, incompressible shearless mixing layers to the parametric variations of ℓ_{1}/ℓ_{2} and E_{1}/E_{2} is investigated. The sensitivity methodology is based on the nonintrusive approach; using direct numerical simulation and generalized polynomial chaos expansion. The analysis is carried out at Re_{ℓ_{1}}=90 for the high-energy HIT region and different integral length scale ratios 1/4≤ℓ_{1}/ℓ_{2}≤4 and turbulent kinetic energy ratios 1≤E_{1}/E_{2}≤30. It is found that the most influential parameter on the variability of the mixing layer evolution is the turbulent kinetic energy while variations of the integral length scale show a negligible influence on the flow field variability. A significant level of anisotropy and intermittency is observed in both large and small scales. In particular, it is found that large scales have higher levels of intermittency and sensitivity to the variations of ℓ_{1}/ℓ_{2} and E_{1}/E_{2} compared to the small scales. Reconstructed response surfaces of the flow field intermittency and the turbulent penetration depth show monotonic dependence on ℓ_{1}/ℓ_{2} and E_{1}/E_{2}. The mixing layer growth rate and the mixing efficiency both show sensitive dependence on the initial condition parameters. However, the probability density function of these quantities shows relatively small solution variations in response to the variations of the initial condition parameters.