Inertial particles driven by a telegraph noise

Abstract

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 particle. The dependence on Stokes and Kubo numbers 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.

8 pages, 6 figures

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Cited by in corpus (13)

• Statistical models for spatial patterns of heavy particles in turbulence
• Statistical models for the dynamics of heavy particles in turbulence
• Stochastic suspensions of heavy particles
• Tangling clustering of inertial particles in stably stratified turbulence
• Distribution of velocity gradients and rate of caustic formation in turbulent aerosols at finite Kubo numbers
• Perturbation theory for a stochastic process with Ornstein-Uhlenbeck noise
• Lyapunov exponents for particles advected in compressible random velocity fields at small and large Kubo numbers
• Weak-strong clustering transition in renewing compressible flows
• Concentration fluctuations of large Stokes number particles in a one-dimensional random velocity field
• Multiple regimes of diffusion
• Heavy particles in a persistent random flow with traps
• Point-source dispersion of quasi-neutrally-buoyant inertial particles
• Density of Inertial Particles: Exactly Solvable 2D Models