Universal statistics of density of inertial particles sedimenting in\n turbulence

2014/09/20 by Itzhak Fouxon, Yongnam Park, Fouxon, Itzhak +5
Earth and Planetary Sciences · Engineering · Environmental Science · #Aeolian processes and effects #Atmospheric aerosols and clouds #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Particle Dynamics in Fluid Flows #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1409.5856

openalex publication_date 2014/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We solve the problem of spatial distribution of inertial particles that\nsediment in Navier-Stokes turbulence with small ratio Fr of acceleration of\nfluid particles to acceleration of gravity g. The particles are driven by\nlinear drag and have arbitrary inertia. We demonstrate that independently of\nthe particles' size or density the particles distribute over fractal set with\nlog-normal statistics determined completely by the Kaplan-Yorke dimension\nD_KY. When inertia is not small D_KY is proportional to the ratio of\nintegral of spectrum of turbulence multiplied by wave-number and g. This\nratio is independent of properties of particles so that the particles\nconcentrate on fractal with universal, particles-independent statistics. We\nfind Lyapunov exponents and confirm predictions numerically. The considered\ncase includes typical situation of water droplets in clouds.\n

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