Rate of formation of caustics in heavy particles advected by turbulence

Abstract

The rate of collision and the relative velocities of the colliding particles in turbulent flows is a crucial part of several natural phenomena, e.g., rain formation in warm clouds and planetesimal formation in a protoplanetary disks. The particles are often modeled as passive, but heavy and inertial. Within this model, large relative velocities emerge due to formation of singularities (caustics) of in the gradient matrix of the velocities of the particles. Using extensive direct numerical simulations of heavy particles in both two (direct and inverse cascade) and three dimensional turbulent flows we calculate the rate of formation of caustics, $J$ as a function of the Stokes number ($\mathrm{St}$).The best approximation to our data is $J\sim \exp (-C/\mathrm{St})$, in the limit $\mathrm{St}\to 0$ where $C$ is a non-universal constant.

Consistent with the version accepted for publication in Philosophical Transactions of the Royal Society A

References in corpus (7)

• The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained
• Caustic activation of rain showers
• Lagrangian dynamics and statistical geometric structure of turbulence
• Sling effect in collisions of water droplets in turbulent clouds
• Unmixing in Random Flows
• Distribution of velocity gradients and rate of caustic formation in turbulent aerosols at finite Kubo numbers
• Paths to caustic formation in turbulent aerosols

Cited by in corpus (6)

• Statistical models for the dynamics of heavy particles in turbulence
• Quantitative prediction of sling events in turbulence at high Reynolds numbers
• 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
• Caustics of finitely dense inertial particles