Analysis of the correlation dimension for inertial particles
- Department of Physics, University of Tor Vergata, 00133 Rome (Italy)
- Department of Physics, Göteborg University, 41296 Gothenburg (Sweden)
- Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA (United Kingdom)
We obtain an implicit equation for the correlation dimension which describes clustering of inertial particles in a complex flow onto a fractal measure. Our general equation involves a propagator of a nonlinear stochastic process in which the velocity gradient of the fluid appears as additive noise. When the long-time limit of the propagator is considered our equation reduces to an existing large-deviation formalism from which it is difficult to extract concrete results. In the short-time limit, however, our equation reduces to a solvability condition on a partial differential equation. In the case where the inertial particles are much denser than the fluid, we show how this approach leads to a perturbative expansion of the correlation dimension, for which the coefficients can be obtained exactly and in principle to any order. We derive the perturbation series for the correlation dimension of inertial particles suspended in three-dimensional spatially smooth random flows with white-noise time correlations, obtaining the first 33 non-zero coefficients exactly.
- OSTI ID:
- 22482468
- Journal Information:
- Physics of Fluids (1994), Vol. 27, Issue 7; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-6631
- Country of Publication:
- United States
- Language:
- English
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