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 $d\gg 1$ 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.

4 pages, RevTex 3.0, Submitted to Phys. Rev. Lett

References in corpus (2)

• ANOMALOUS SCALING OF THE PASSIVE SCALAR
• Normal and Anomalous Scaling of the Fourth-Order Correlation Function of a Randomly Advected Passive Scalar

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