Lagrangian and Eulerian descriptions of inertial particles in random flows

Abstract

We study how the spatial distribution of inertial particles evolves with time in a random flow. We describe an explosive appearance of caustics and show how they influence an exponential growth of clusters due to smooth parts of the flow, leading in particular to an exponential growth of the average distance between particles. We demonstrate how caustics restrict applicability of Lagrangian description to inertial particles.

Keywords:

• Two-phase flows
• Inertial particles
• Lyapunov exponents
• Caustics

Acknowledgement

The work was supported by the Israeli Science Foundation, the EPSRC and the Royal Society.