Simulations of a randomly advected passive scalar field

The advection of a passive scalar field by a rapidly decorrelating random velocity field with power-law scaling is computed by simulations in a cyclic square at resolutions of ${4096}^2$ and ${8192}^2$ grid points. Structure functions of the scalar field are measured and inertial-range scaling exponents are determined. The conditional mean of the scalar-field dissipation term and its moments are found. The results are compared with theoretical predictions and with other recent simulations.