Inertial particles driven by a telegraph noise.
We present a model for the Lagrangian dynamics of inertial particles in a compressible flow, where fluid velocity gradients are modeled 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 the Stokes number St and the Kubo number Ku of the Lyapunov exponent of particle trajectories reveals the presence of a region in parameter space (St, Ku), where the leading Lyapunov exponent changes sign, thus signaling the transition. The asymptotics of short- and long-correlated flows are discussed, as well as the fluid-tracer limit.
Falkovich
G
G
Weizmann Institute of Science, Rehovot, 76100 Israel.
Musacchio
S
S
Piterbarg
L
L
Vucelja
M
M