# Heavy particles in a persistent random flow with traps

## TL;DR

This paper models heavy particles in a one-dimensional compressible fluid with persistent Gaussian velocity fields, analyzing trapping, Lyapunov exponents, and caustic formation, with implications for higher-dimensional systems.

## Contribution

It introduces a novel analytical framework for understanding particle trapping and caustic formation in a 1D compressible flow with weak inertia.

## Key findings

- Particles tend to accumulate in trapping regions.
- Analytical expressions for Lyapunov exponents and caustic rates are derived.
- Numerical simulations confirm the analytical predictions.

## 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.