| 講演要旨： |
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 can cluster. I analyse this 'unmixing' effect by calculating the Lyapunov exponents for dense particles suspended in 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, in 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. The series expansion can be automated, and we report results for the first six orders. The perturbation series is divergent, but we obtain accurate results from a Pade-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 using Navier-Stokes flows. We also investigate the rate of formation of caustics in the particle flow.
This work was done in collaboration with Bernhard Mehlig, Stellan Ostlund and Kevin Duncan. An account of the work has appeared in Physical Review Letters, 95, 240602, (2005).
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