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 ≫ 1 is considered.Scaling exponents of the scalar field are analytically found to be ζ 2n = n ζ 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 ≪d.The refined similarity hypothesis ζ 2n = n ζ 2 + μ n is thus established by a straightforward calculation for the case considered.