The formation of Pareto distribution in tracer systems on the water surface

TL;DR

This study experimentally demonstrates that a Pareto distribution naturally forms in the clustering of tracers on water surfaces, influenced by surface tension and background flows, revealing insights into surface structure dynamics.

Contribution

It is the first experimental analysis showing Pareto distribution formation in tracer clustering on water surfaces and the role of background flows in this process.

Findings

Pareto distribution describes cluster density on water surface

Surface tension influences surface structure growth

Background flows significantly affect clusterization

Abstract

We experimentally studied a clusterization process in a system of polyamide tracers that are used for visualizing the flow of liquids on their surface. It was shown that in a surface structure system appearing on the water surface a Pareto distribution is formed for normalized cluster density and it is well described by a C/x^(-n) power-law function. One can suggest that the growth of a surface structure is defined by the action of surface tension forces, and the number of surface structures decreases exponentially, while maintaining their total surface area. We show experimentally the significant role of background liquid flows on the surface in the clusterization process