**Inertial Particles Driven
by a Telegraph Noise**

Marija Vucelja, Weizmann
Institute of Science, Courant Institute of Science

Abstract:

I will introduce a model for the Lagrangian
dynamics of inertial particles in a compressible flow with temporal
correlations (the velocity gradients were modeled with telegraph noise). This
model is analytically tractable and as such it represents the first attempt to describe
the clustering of particles, due to inertia, in the presence of
temporal correlations of the
velocity field. Extensions of the model, could bring
us closer to describing rain formation, clustering of dust in air etc. I will
discuss the asymptotic of short and long-correlated flows, as well as the
fluid-tracer limit. One of the results in this work is the dependence of the Lyapunov exponent of particle trajectories on dimensionless
parameters of the model. It revealed the presence of a region in parameter
space, where the Lyapunov exponent changes sign, thus
signaling the the aggregation-disorder transition of
inertial particles.