Anomalous Scaling Exponents of a White-Advected Passive Scalar

For Kraichnan's problem of passive scalar advection by a velocity field delta-correlated in time, the limit of large space dimensionality $d\gg1$ is considered. Scaling exponents of the scalar field are analytically found to be $\zeta_{2n}=n\zeta_2-2(2-\zeta_2)n(n-1)/d$, while those of the dissipation field are $\mu_{n}=-2(2-\zeta_2)n(n-1)/d$ for orders $n\ll d$. The refined similarity hypothesis $\zeta_{2n}=n\zeta_2+\mu_{n}$ is thus established by a straightforward calculation for the case considered.Comment: 4 pages, RevTex 3.0, Submitted to Phys. Rev. Let

Two complementary descriptions of intermittency

We describe two complementary formalisms designed for the description of probability density function (PDF) of the gradients of turbulent fields. The first approach, we call it adiabatic, describes PDF at the values much less than dispersion. The second, instanton, approach gives the tails of PDF at the values of the gradient much larger than dispersion. Together, both approaches give satisfactory description of gradient PDFs, as illustrated here by an example of a passive scalar advected by a one-dimensional compressible random flow.Comment: 4 pages, RevTeX, submitted to PR