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Inertial particles driven by a telegraph noise.

Research paper by G G Falkovich, S S Musacchio, L L Piterbarg, M M Vucelja

Indexed on: 13 Oct '07Published on: 13 Oct '07Published in: Physical review. E, Statistical, nonlinear, and soft matter physics



Abstract

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.