Clustering of floating tracers in weakly divergent velocity fields

This work deals with buoyant tracers floating at the ocean surface, where the geostrophic velocity component is 2D and rotational (non-divergent), and the ageostrophic component can contain comparable in size rotational and potential (divergent) contributions. We consider a random kinematic flow model and study the process of clustering, that is, aggregation of the floating tracer in localized spatial patches. In the large-time limit, and in the cases of strongly and weakly divergent flows, the existing analytical theory predicts the process of exponential clustering, which is the emergence of spatial singularities containing all the available tracer. Here, we confirm this analytical prediction, in numerical model solutions spanning different combinations of rotational and potential surface velocity components, and report that exponential clustering persists even in weakly divergent flows, however, at significantly slower rates. For a wide range of parameters, we analyzed not only the exponential clustering, but also the other type of tracer aggregation, referred to as fragmentation clustering, as well as the coarse-graining effects on clustering. For the presented analyses we considered ensembles of Lagrangian particles, and introduced and applied the statistical topography methodology