We investigate statistical properties of the passive scalar mixing in random (turbulent) flows assuming diffusion to be weak. Then at advanced stages of the passive scalar decay, its unmixed residue is primarily concentrated in a narrow diffusive layer near the wall and its transport to the bulk goes through the peripheral region (laminar sublayer of the flow).
We conducted Lagrangian numerical simulations of the process for different space dimensions and revealed structures responsible for the transport, which are passive scalar tongues pulled from the diffusive boundary layer to the bulk. We investigated statistical properties of the passive scalar and of the passive scalar integrated along the wall. Moments of both objects demonstrate scaling behavior outside the diffusive boundary layer.
We propose an analytic scheme for the passive scalar statistics, explaining the features observed numerically. We extend our consideration to inertial particles and reveal their confinement in the boundary layer.