Geometric features of the mixing of passive scalars at high Schmidt numbers.

The mixing of passive scalars of decreasing diffusivity, advected in each case by the same three-dimensional Navier-Stokes turbulence, is studied. The mixing becomes more isotropic with decreasing diffusivity. The local flow in the vicinity of steepest negative and positive scalar gradients is in general different, and its behavior is studied for various values of the scalar diffusivity. Mixing approaches monofractal properties with diminishing diffusivity. We consider these results in the context of possible singularities of scalar dissipation.