Correlation Dimension of Inertial Particles in Random Flows

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.

4 pages, 1 figure

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• Heavy particle concentration in turbulence at dissipative and inertial scales
• Lyapunov exponents of heavy particles in turbulence
• Unmixing in Random Flows
• Stochastic suspensions of heavy particles
• Stokes trapping and planet formation

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