ANOMALOUS SCALING IN PASSIVE SCALAR ADVECTION - MONTE-CARLO LAGRANGIAN TRAJECTORIES

We present a numerical method which is used to calculate anomalous sca ling exponents of structure functions in the Kraichnan passive scalar advection model [R.H. Kraichnan, Phys. Fluids Il, 945 (1968)]. This Mo nte Carlo method, which is applicable in any space dimension, is based on the Lagrangian path interpretation of passive scalar dynamics, and uses the recently discovered equivalence between scaling exponents of structure functions and relaxation rates in the stochastic shape dyna mics of groups of Lagrangian particles. We calculate third and fourth order anomalous exponents for several dimensions, comparing with the p redictions of perturbative calculations in large dimensions. We find t hat Kraichnan's closure appears to give results in close agreement wit h the numerics. The third order exponents are compatible with our own previous nonperturbative calculations.