  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.
