Intermittent distribution of tracers advected by a compressible random flow

Multifractal properties of a tracer density passively advected by a compressible random velocity field are characterized. A relationship is established between the statistical properties of mass on the dynamical fractal attractor towards which the trajectories converge and large deviations of the stretching rates of the flow. In the framework of the compressible Kraichnan model, this result is illustrated by analytical calculations and confirmed by numerical simulations.