Power-law distributions of particle concentration in free-surface flows

TL;DR

This study investigates how particles on a turbulent fluid surface cluster along string-like structures, revealing a power-law distribution of particle concentration that varies across different flow scales.

Contribution

It provides the first detailed analysis of the scale-dependent power-law distribution of particle concentrations in free-surface turbulent flows.

Findings

Particle concentrations follow a power-law distribution with a peak at zero.

The exponent of the power-law decreases with scale in the inertial range.

Distinct behaviors are observed between dissipative and inertial flow ranges.

Abstract

Particles floating on the surface of a turbulent incompressible fluid accumulate along string-like structures, while leaving large regions of the flow domain empty. This is reflected experimentally by a very peaked probability distribution function of $c_r$, the coarse-grained particle concentration at scale $r$, around $c_r = 0$, with a power-law decay over two decades of $c_r$, $\Pi (c_r) \propto c_r^{-\beta_r}$. The positive exponent $\beta_r$ decreases with scale in the inertial range, and stays approximately constant in the dissipative range, thus indicating a qualitative difference between the dissipative and the inertial ranges of scales, also visible in the first moment of $c_r$.