Statistically Preserved Structures and Anomalous Scaling in Turbulent Active Scalar Advection

Abstract

The anomalous scaling of correlation functions in the turbulent statistics of active scalars (like temperature in turbulent convection) is understood in terms of an auxiliary passive scalar which is advected by the same turbulent velocity field. While the odd-order correlation functions of the active and passive fields differ, we propose that the even-order correlation functions are the same to leading order (up to a trivial multiplicative factor). The leading correlation functions are statistically preserved structures of the passive scalar decaying problem, and therefore universality of the scaling exponents of the even-order correlations of the active scalar is demonstrated.