(in collaboration with M. Wilkinson)
We consider particles suspended in a turbulent fluid. When effects of
the
inertia of the particles are significant, an initially uniform scatter
of
particles can cluster together. We analyse 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 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 in simulations of turbulent
Navier-Stokes flows. We also investigate the rate of formation of
caustics
in the particle flow, as well as their rate of collision. We discuss
implications for the problem of rain initiaion by turbulence and planet
formation in turbulent accretion disks.
Refs:
arXiv:0706.3536
arXiv:nlin/0702024
arXiv:nlin/0612061
arXiv:nlin/0612008