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We investigate statistical properties of the passive scalar near boundaries(walls) in random (turbulent) flows assuming weakness of its diffusion. Then atadvanced stages of the passive scalar mixing its unmixed residue isconcentrated in a narrow diffusive layer near the wall and its transport tobulk goes through the peripheral region (laminar sublayer). We conductedLagrangian numerical simulations of the process for different space dimensions$d$ and revealed structures responsible for the transport that are passivescalar tongues pulled from the diffusive boundary layer to bulk. Weinvestigated statistical properties of the passive scalar and of the passivescalar integrated along the wall. Moments of both objects demonstrate scalingbehavior outside the diffusive boundary layer. We propose an analytical schemefor explanation scaling of the passive scalar, the obtained exponents agreereasonably with numerics in 3d.

Passive scalar transport in peripheral regions of random flows