Heavy particles in a persistent random flow with traps
arXiv:1902.04354 · doi:10.1103/PhysRevE.100.023102
The paper analyzes a one‑dimensional model of heavy particles moving in a compressible, persistent Gaussian random flow, focusing on how particles become trapped, the resulting Lyapunov exponent, and the rate of caustic formation.
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.
8 pages, 4 figures, published version