Direct numerical simulations of the Kraichnan model: Scaling exponents and fusion rules

We present results from direct numerical simulations of the Kraichnan model for passive scalar advection by a rapidly varying random scaling velocity field for intermediate values of the velocity scaling exponent. These results are compared with the scaling exponents predicted for this model by Further, we test the recently proposed fusion rules which govern the scaling properties of multipoint correlations, and present results on the linearity of the conditional statistics of the Laplacian operator on the scalar field.