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Analysis of the correlation dimension for inertial particles

Artikel i vetenskaplig tidskrift
Författare Kristian Gustavsson
Bernhard Mehlig
M. Wilkinson
Publicerad i Physics of Fluids
Volym 27
Nummer/häfte 7
Sidor article Number: 073305
ISSN 1070-6631
Publiceringsår 2015
Publicerad vid Institutionen för fysik (GU)
Sidor article Number: 073305
Språk en
Länkar dx.doi.org/10.1063/1.4927220
Ämnesord ISOTROPIC TURBULENCE, HEAVY-PARTICLES, INTERMITTENT DISTRIBUTION, AEROSOL-PARTICLES, RANDOM FLOWS, STOKES, MOTION, FIELDS, FLUID, Mechanics, Physics, Fluids & Plasmas
Ämneskategorier Fysik

Sammanfattning

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. (C) 2015 AIP Publishing LLC.

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