Self-similarity of scalar iso-surface area density in a temporal mixing layer

In many turbulent flows, distinct regions of the flow are separated by sharp interfaces that can be described by iso-surfaces of a scalar field. Examples include the stoichiometric value of the mixture fraction in non-premixed combustion, and a small threshold value of the vorticity magnitude for the turbulent/non-turbulent interface. Recent developments in computer hardware and software now allow for in-depth analysis of the characteristics of these interfaces. This talk discusses the direct numerical simulation of a turbulent, temporally developing mixing layer using GPU resources on the Lassen supercomputer at Lawrence Livermore National Laboratory. A novel software approach has been used to calculate the mean surface area density, Σ, as a function of the cross-stream position. We find that, in addition to the velocity field statistics, the cross-stream profiles of Σ and related quantities also become self-similar. Preliminary results suggest that the self-similarity variable for Σ scales with the Taylor microscale. We also investigate the transport equation for Σ as a function of the cross-stream position, and analyze the resulting terms related to area production, destruction, advection/diffusion and their effects on iso-surface growth within the self-similar period.