Abstract for "Inertial particles driven by a telegraph noise":
The spontaneous formation of clusters of particles suspended in
chaotic flows may originate from two different physical processes:
compressibility of the fluid flow and particle inertia. In the
first case particles are trapped in regions of ongoing
compression, while in the second case inertia causes their
ejection from vortical regions.
The interplay of these two mechanisms may lead to unexpected
consequences. In particular, in compressible flows, where fluid
trajectories coalesce, large enough inertia can induce a transition
from the strong clustering regime into a week clustering one, where
particle trajectories remains chaotic.
We present a model for the Lagrangian dynamics of inertial particles in
a compressible flow, where fluid velocity gradients are modelled by a
telegraph noise. The model allows for an analytic investigation of the
role of time correlation of the flow in the aggregation--disorder
transition of inertial particles. The dependence on Stokes and Kubo
numbers of the Lyapunov exponent of particle trajectories reveals the
presence of a region in parameter space where the leading Lyapunov
exponent changes sign, thus signaling the transition.