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arXiv · 0909.0955

Correlation Dimension of Inertial Particles in Random Flows

Michael Wilkinson·Bernhard Mehlig·Kristian Gustavsson
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Abstract

We obtain an implicit equation for the correlation dimension of dynamical systems in terms of an integral over a propagator. We illustrate the utility of this approach by evaluating the correlation dimension 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 the correlation dimension 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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Michael Wilkinson, Bernhard Mehlig, Kristian Gustavsson. 2009-09-04. Correlation Dimension of Inertial Particles in Random Flows. https://doi.org/10.1209/0295-5075%2F89%2F50002

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