Inhomogeneous distribution of droplets in cloud turbulence

Abstract

We solve the problem of spatial distribution of inertial particles that sediment in turbulent flow with small ratio of acceleration of fluid particles to acceleration of gravity $g$. The particles are driven by linear drag and have arbitrary inertia. The pair-correlation function of concentration obeys a power-law in distance with negative exponent. Divergence at zero signifies singular distribution of particles in space. Independently of particle size the exponent is ratio of integral of energy spectrum of turbulence times the wavenumber to $g$ times numerical factor. We find Lyapunov exponents and confirm predictions by direct numerical simulations of Navier-Stokes turbulence. The predictions include typical case of water droplets in clouds. This significant progress in the study of turbulent transport is possible because strong gravity makes the particle's velocity at a given point unique.

6 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1409.5856, text revisions

References in corpus (6)

• Heavy particle concentration in turbulence at dissipative and inertial scales
• Caustic activation of rain showers
• Sling effect in collisions of water droplets in turbulent clouds
• Lyapunov exponents of heavy particles in turbulence
• Quantifying turbulence induced segregation of inertial particles
• Gravity-driven clustering of inertial particles in turbulence

Cited by in corpus (7)

• The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part II: Simulations with gravitational effects
• On phoretic clustering of particles in turbulence
• Inertial particles distribute in turbulence as Poissonian points with random intensity inducing clustering and supervoiding
• Quantitative prediction of sling events in turbulence at high Reynolds numbers
• Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence
• The effect of a wall on the interaction of two spheres in shear flow: Batchelor-Green theory revisited
• Inhomogeneous preferential concentration of inertial particles in turbulent channel flow