Correlation dimension of inertial particles in random flows

Wilkinson, M.; Mehlig, B. and Gustavsson, K. (2010). Correlation dimension of inertial particles in random flows. Europhysics Letters, 89(5) p. 50002.

DOI: https://doi.org/10.1209/0295-5075/89/50002

Abstract

We obtain an implicit equation for the correlation dimension D2 of dynamical systems in terms of an integral over a propagator. We illustrate the utility of this approach by evaluating D2 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 D2 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.

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