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 d1 is considered. Scaling exponents of the scalar field are analytically found to be ζ₂ₙ0ex0ex=0ex0exnζ₂-2(2-ζ₂)n(n-1)/d, while those of the dissipation field are μₙ0ex0ex=0ex0ex-2(2-ζ₂)n(n-1)/d for orders nd. The refined similarity hypothesis ζ₂ₙ0ex0ex=0ex0exnζ₂+μₙ is thus established by a straightforward calculation for the case considered.