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Unmixing in random flows

Wilkinson, M.; Mehlig, B.; Ostlund, S. and Duncan, K. P. (2007). Unmixing in random flows. Physics of Fluids, 19 p. 113303.

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We consider particles suspended in a randomly stirred or turbulent fluid. When effects of the inertia of the particles are significant, an initially uniform scatter of particles can cluster together. We analyze this “unmixing” effect by calculating the Lyapunov exponents for dense particles suspended in such a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time of the random flow (that is, the regime of large Stokes number). In this limit Lyapunov exponents are obtained as a power series in a parameter which is a dimensionless measure of the inertia. We report results for the first seven orders. The perturbation series is divergent, but we obtain accurate results from a Padé-Borel summation. We deduce that particles can cluster onto a fractal set and show that its dimension is in satisfactory agreement with previously reported simulations of turbulent Navier-Stokes flows. We also investigate the rate of formation of caustics in the particle flow

Item Type: Journal Item
Copyright Holders: 2007 American Institute of Physics
ISSN: 1070-6631
Extra Information: Article is 23 pages long
Keywords: Lyapunov methods; Navier-Stokes equations
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 25383
Depositing User: Michael Wilkinson
Date Deposited: 03 Mar 2011 10:20
Last Modified: 07 Dec 2018 09:45
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