LAGRANGIAN PATH-INTEGRALS AND FLUCTUATIONS IN RANDOM FLOW

The problem of the asymptotic behavior of the probability distribution function (PDF) of a scalar field advected by Gaussian random flow is investigated using the Lagrangian path-integral approach, which naturally captures the physics of transport and dissipation relevant to the problem. For a single-scale random-velocity field and in the presence of a mean scalar gradient we find that the one-point PDFs of both the scalar and its gradient have exponential tails. Under the same conditions the normalized gradient skewness scales with Peclet number to approximately -0.3 power.