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Anomalous scaling behaviour of a passive scalar in the presence of a mean gradient

The problem of mixing of a passive scalar by a Gaussian, isotropic, random velocity field, decorrelated in time, and with a power law scaling of the velocity differences as |x|ζ/2 is considered. In the presence of an imposed mean scalar gradient, the existence of an anomalous scaling exponent of the three-point correlation function is established. The exponent is explicitly computed in perturbation for small values of ζ. The result provides a qualitative explanation of several experimental and numerical observations.