Distribution of particles and bubbles in turbulence at small Stokes number

TL;DR

This paper analyzes how particles of different densities distribute in turbulent flows, revealing their tendency to cluster in specific regions and characterizing their spatial distribution using fractal and correlation measures.

Contribution

It provides an analytical description of particle distribution in turbulence, deriving correlation functions and fractal dimensions based on recent chaotic dynamics results.

Findings

Particles preferentially concentrate in regions of low vorticity or high vorticity depending on their density.

Distribution forms a multi-fractal attractor in space.

Results are applicable to real turbulence and can be tested experimentally.

Abstract

The inertia of particles driven by the turbulent flow of the surrounding fluid makes them prefer certain regions of the flow. The heavy particles lag behind the flow and tend to accumulate in the regions with less vorticity, while the light particles do the opposite. As a result of the long-time evolution, the particles distribute over a multi-fractal attractor in space. We consider this distribution using our recent results on the steady states of chaotic dynamics. We describe the preferential concentration analytically and derive the correlation functions of density and the fractal dimensions of the attractor. The results are obtained for real turbulence and are testable experimentally.