Correlation dimension of inertial particles in random flows

¹  Department of Mathematics and Statistics, The Open University - Walton Hall, Milton Keynes, MK7 6AA, England, UK
²  Department of Physics, Gothenburg University - 41296 Gothenburg, Sweden

Corresponding author: m.wilkinson@open.ac.uk

Received: 23 November 2009
Accepted: 12 February 2010

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.