# Clustering of floating tracers in weakly divergent velocity fields

## TL;DR

This paper investigates how floating tracers cluster in weakly divergent ocean surface flows, extending existing theories to include combined flow components and analyzing the effects on clustering rates and patterns.

## Contribution

It extends asymptotic clustering theory to weakly divergent flows by analyzing combined flow components and introduces statistical topography for systematic clustering studies.

## Key findings

- Complete clustering persists even in weakly divergent flows but at a slower rate.
- Clustering behavior depends on the combination of solenoidal and potential flow components.
- Methodology enables systematic analysis of clustering in complex flow regimes.

## Abstract

This work focuses on buoyant tracers floating on the ocean surface and treats the geostrophic and ageostrophic surface velocities as the 2D solenoidal (non-divergent) and potential (divergent) flow components, respectively. We consider a random kinematic flow model and study the process of clustering, that is, aggregation of tracers in localized spatial patches. An asymptotic theory exists only for strongly divergent velocity fields and predicts complete clustering, that is, emergence in the large-time limit of spatial singularities containing all available tracers. To extend the theory, we consider combinations of the solenoidal and potential velocity components and explore the corresponding regimes of the clustering process. We have found that, even for weakly divergent flows complete clustering still persists but occurs at a significantly slower rate. For a wide range of parameters, we have analyzed this process, as well as the other type of clustering, referred to as fragmentation clustering, and the coarse-graining effects on clustering, and interpreted the results. For the analyses we have considered ensembles of Lagrangian particles representing the tracer, then, introduced and applied the methodology of statistical topography, which paves the way for systematic studies of clustering in progressively more complicated flows, and for both passive and floating tracers.