NORMAL AND ANOMALOUS SCALING OF THE 4TH-ORDER CORRELATION-FUNCTION OFA RANDOMLY ADVECTED PASSIVE SCALAR

For a short-correlated velocity field, simultaneous correlation functi ons of a passive scalar satisfy closed equations. We analyze the equat ion for the four-point function. To describe a solution completely, on e has to solve the matching problems at the scale of the source and at the diffusion scale. We solve both the matching problems and thus fin d the dependence of the four-point correlation function on the diffusi on and pumping scale for large space dimensionality d. It is shown tha t anomalous scaling appears in the first order of lid perturbation the ory. Anomalous dimensions are found analytically both for the scalar h eld and for its derivatives, in particular, for the dissipation held.