Correlation dimension of inertial particles in random flows
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: email@example.com
Accepted: 12 February 2010
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.45.-a – Nonlinear dynamics and chaos
© EPLA, 2010