Anomalous scaling in theN-point functions of a passive scalar

A recent analysis of the four-point correlation function of the passive scalar advected by a time-decorrelated random flow is extended to the N-point case. It is shown that all stationary-state inertial-range correlations are dominated by homogeneous zero modes of singular operators describing their evolution. We compute analytically the zero modes governing the N-point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the two-point function of the advecting velocity field. The implications of these calculations for the dissipation correlations are discussed. {} 1996 The American Physical Society.