Passive scalar structures in peripheral regions of random flows

We investigate statistical properties of the passive scalar near walls in random flows assuming weakness of its diffusion. Then at advanced stages of the passive scalar mixing its unmixed residue is concentrated in a narrow diffusive layer near the wall. We conducted numerical simulations and revealed structures responsible for the passive scalar transport to bulk, they are passive scalar tongues pulled from the diffusive boundary layer. The passive scalar integrated along the wall possesses well pronounced scaling behavior. We propose an analytical scheme giving exponents of the integral passive scalar moments, the exponents agree reasonably with numerics in $3d$.