DNS of mixing in spatially developing shear layers

The majority of models proposed for turbulent combustion rely on the knowledge of the mixture fraction $Z$, its pdf, the scalar dissipation, and, in some cases, a mixing time scale. Turbulent mixing in technical devices is almost always inhomogeneous and the flow regime is transitional so that spatially developing mixing layers are highly relevant. DNS have been performed for a Reynolds number up to $2 \times 10^4$, enough to identify mixing transition. All relevant statistics and their dependence on Reynolds number have been analyzed. Previous results show that the scalar pdf can be: {\it non-marching}, when the most probable value of the mixture fraction of mixed fluid is invariant across the width of the layer; {\it marching}, for which the most probable value is the mean mixture fraction at the location considered. The pdf behavior is discussed in several previous works and it has been found to be related to the Reynolds number and the level of turbulence development. The DNS results we present clearly show that the pdf evolves from {\it non-marching} to {\it marching} during the streamwise evolution of the scalar field.