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arXiv · 1409.5856

Universal statistics of density of inertial particles sedimenting in turbulence

Itzhak Fouxon·Yongnam Park·Roei Harduf·Changhoon Lee
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Abstract

We solve the problem of spatial distribution of inertial particles that sediment in Navier-Stokes turbulence with small ratio $Fr$ of acceleration of fluid particles to acceleration of gravity $g$. The particles are driven by linear drag and have arbitrary inertia. We demonstrate that independently of the particles' size or density the particles distribute over fractal set with log-normal statistics determined completely by the Kaplan-Yorke dimension $D_{KY}$. When inertia is not small $D_{KY}$ is proportional to the ratio of integral of spectrum of turbulence multiplied by wave-number and $g$. This ratio is independent of properties of particles so that the particles concentrate on fractal with universal, particles-independent statistics. We find Lyapunov exponents and confirm predictions numerically. The considered case includes typical situation of water droplets in clouds.

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Itzhak Fouxon, Yongnam Park, Roei Harduf, Changhoon Lee. 2014-10-30. Universal statistics of density of inertial particles sedimenting in turbulence. https://arxiv.org/abs/1409.5856

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