Signatures of fractal clustering of aerosols advected under gravity

TL;DR

This paper identifies two fractal signatures in the chaotic advection of aerosols under gravity, allowing the determination of the attractor's fractal dimension from limited observational data, with implications for meteorology.

Contribution

It introduces two novel fractal signatures that enable calculating the fractal dimension of aerosol attractors from data at a single level, advancing understanding of aerosol dynamics.

Findings

Two fractal signatures enable fractal dimension computation from single-level data.

Numerical experiments validate the theoretical signatures.

Potential applications in meteorological data analysis.

Abstract

Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical situations, observational data may be available only at a given level, for example at the ground level. We uncover two fractal signatures of chaotic advection of aerosols under the action of gravity. Each one enables the computation of the fractal dimension $D_{0}$ of the strange attractor governing the advection dynamics from data obtained solely at a given level. We illustrate our theoretical findings with a numerical experiment and discuss their possible relevance to meteorology.