Heavy particles in a persistent random flow with traps

Abstract

We study a one-dimensional model for heavy particles in a compressible fluid. The fluid-velocity field is modelled by a persistent Gaussian random function, and the particles are assumed to be weakly inertial. Since one-dimensional fluid-velocity fields are always compressible, the model exhibits spatial trapping regions where particles tend to accumulate. We determine the statistics of fluid-velocity gradients in the vicinity of these traps and show how this allows to determine the spatial Lyapunov exponent and the rate of caustic formation. We compare our analytical results with numerical simulations of the model and explore the limits of validity of the theory. Finally, we discuss implications for higher-dimensional systems.

arXiv comment8 pages, 4 figures, published version

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Cited by in corpus (4)

• Theory for the effect of fluid inertia on the orientation of a small particle settling in turbulence
• Caustics in turbulent aerosols form along the Vieillefosse line at weak particle inertia
• Caustic formation in a non-Gaussian model for turbulent aerosols
• Dissecting inertial clustering and sling dynamics in high-Reynolds number particle-laden turbulence