Three-point statistics of passive scalars at high Schmidt numbers

The turbulent mixing of passive scalars is a fundamental problem relevant to many natural and engineering flows. While traditionally analyzed via one- or two-point statistics, three-point statistics have also been used to gain insight into the structure of the scalar field [Warhaft, {\it Annu. Rev. Fluid Mech} {\bf 32}, 203--240 (2000)]. Experimental data are scarce, and for the important case of scalar fluctuations generated under the presence of a mean gradient in isotropic turbulence, measurements are limited to Schmidt numbers ($Sc$) near unity [Mydlarski and Warhaft, {\it Phys. Fluids} {\bf 10}, 2885--2894 (1998)]. Here we analyze three-point statistics from direct numerical simulations of scalars under a uniform mean gradient in $R_\lambda\approx 140$ forced isotropic turbulence. By using grids with up to $8192^3$ points and passive scalars with $Sc$ up to 512, three-point statistics are gathered in the emerging viscous-convective range to study the approach to local isotropy exhibited by high-$Sc$ scalars.