Correlation dimension of inertial particles in random flows

We obtain an implicit equation for the correlation dimension D(2) of dynamical systems in terms of an integral over a propagator. We illustrate the utility of this approach by evaluating D(2) for inertial particles suspended in a random flow. In the limit where the correlation time of the flow field approaches zero, taking the short-time limit of the propagator enables D(2) to be determined from the solution of a partial differential equation. We develop the solution as a power series in a dimensionless parameter which represents the strength of inertial effects. Copyright (C) EPLA, 2010