Lagrangian method for multiple correlations in passive scalar advection

A Lagrangian method is introduced for calculating simultaneous n-point correlations of a passive scalar advected by a random velocity field, with random forcing and finite molecular diffusivity κ. The method, which is here presented in detail, is particularly well suited for studying the κ→0 limit when the velocity field is not smooth. Efficient Monte Carlo simulations based on this method are applied to the Kraichnan model of passive scalar and lead to accurate determinations of the anomalous intermittency corrections in the fourth-order structure function as a function of the scaling exponent ξ of the velocity field in two and three dimensions. Anomalous corrections are found to vanish in the limits ξ→0 and ξ→2, as predicted by perturbation theory.