On the kinematics of scalar iso-surfaces in turbulent flow

The behavior of scalar iso-surfaces in turbulent flows is of fundamental interest and importance in a number of problems, e.g., the stoichiometric surface in non-premixed reactions, and the turbulent/non-turbulent interface in localized turbulent shear flows. Of particular interest here is the behavior of the average surface area per unit volume, $\Sigma$. We report on the use of direct numerical simulations and sophisticated surface tracking techniques to directly compute $\Sigma$ and model its evolution. We consider two different scalar configurations in decaying, isotropic turbulence: first, the iso-surface is initially homogenous and isotropic in space, second, the iso-surface is initially planar. A novel method of computing integral properties from regularly-sampled values of a scalar function is leveraged to provide accurate estimates of $\Sigma$. Guided by simulation results, modeling is introduced from two perspectives. The first approach models the various terms in the evolution equation for $\Sigma$, while the second uses Rice’s theorem to model $\Sigma$ directly. In particular, the two principal effects on the evolution of $\Sigma$, i.e., the growth of the surface area due to local surface stretching, and the ultimate decay due to molecular destruction, are addressed.