Inertial Particles Driven by a Telegraph Noise

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



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.