Clustering of floating tracers in weakly divergent velocity fields

Abstract

This work focuses on buoyant tracers floating on the ocean surface and treats the geostrophic and ageostriphic 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.

Clustering of Floating Tracer Due to Mesoscale Vortex and Submesoscale Fields

“…To quantify clustering properties in the above‐discussed scenarios, we make use of statistical topography diagnostics, such as the clustering area and mass. In EXP4, the rate of exponential clustering (Figure ) is qualitatively similar to but still slower to the theoretical prediction for the purely divergent case EXP3 (Klyatskin, ; Klyatskin & Koshel, ; Koshel et al, ). Despite the general tendency towards the exponential clustering, the clustering process is significantly affected by the specifics of the regular velocity, as illustrated by different evolution curves for different locations of the initial tracer deployment (Figure ).…”

“…The asymptotic theory of clustering in random velocity fields (Klyatskin, ) states that the exponential clustering occurs necessarily, if the divergent velocity component completely dominates over the rotational one. When both components are comparable, the exponential clustering persists but its properties become significantly altered (Koshel et al, )—this result is, however, restricted to specific and purely kinematic velocities. The main novelty of the present work is in relaxing this restriction by dynamically constraining the mesoscale flow component, which is referred to as the regular component.…”

Floating tracer clustering in divergent random flows modulated by an unsteady mesoscale ocean field

“…The resulting clustering process is ultimately induced by the velocity divergence (Klyatskin et al 1996b,a, Saichev and Woyczynski 1996, Falkovich et al 2001, Eckhardt and Schumacher 2001, Schumacher and Eckhardt 2002, Cressman and Goldburg 2003, Bec et al 2004, Fouxon 2012, Klyatskin 2015, Huntley et al 2015, Jacobs et al 2016, Klyatskin 2016, Väli et al 2018. Our previous papers dealt with clustering in kinematic, zero-mean, random velocity fields (Koshel et al 2019b), and also in such fields with the additional, deterministic, steady velocity component represented by realistic mesoscale flow features (Stepanov et al 2020). The present work generalises and extends the previous results by considering a more complex, unsteady time-dependent mesoscale flow component and its influence on the clustering processes.…”

“…Because of the many scales of motion involved, the resulting tracer patterns often exhibit spatial inhomogeneities with sharp local aggregations of tracer (Okubo 1980, McComb 1990, Law et al 2010, Cozar et al 2014, Martinez et al 2009, Maximenko et al 2012, Väli et al 2018) that survive for long times. This effect is called clustering and attributed to the effect of the surface velocity divergence (Klyatskin et al 1996a, Koshel and Alexandrova 1999, Klyatskin and Koshel 2000, Huntley et al 2015, Jacobs et al 2016, Koshel et al 2019b, Stepanov et al 2020 on the scales by orders of magnitude smaller than those of the dynamically dominant, coherent mesoscale eddies. The main objective of this paper is to show that the clustering process can be significantly and nontrivially altered by the interplay between the mesoscale and submesoscale velocity components.…”

Relative Dispersion on the Inner Shelf: Evidence of a Batchelor Regime

“…For surface trapped tracer, convergent motions at the surface lead to spatially localized tracer concentrations (e.g., Okubo 1980;Maximenko et al 2012;D'Asaro et al 2018). For various flow situations, various clustering rates due to convergent motions have been estimated using a variety of methods (e.g., Huntley et al 2015;Gutiérrez and Aumaître 2016;Koshel et al 2019). How convergence and divergence affects surface drifter dispersion is not well understood, however, the presence of convergence/divergence may affect the dispersion relative to RO scaling (Cressman et al 2004).…”