Anomalous Scaling Exponents of a White-Advected Passive Scalar

Abstract

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 $ζ_{2n}=nζ_2-2(2-ζ_2)n(n-1)/d$, while those of the dissipation field are $μ_{n}=-2(2-ζ_2)n(n-1)/d$ for orders $n\ll d$. The refined similarity hypothesis $ζ_{2n}=nζ_2+μ_{n}$ is thus established by a straightforward calculation for the case considered.