Clustering of floating tracers in weakly divergent velocity fields

Konstantin V. Koshel, Dmitry V. Stepanov, Eugene A. Ryzhov, Pavel Berloff, and V. I. Klyatskin
Phys. Rev. E 100, 063108 – Published 20 December 2019

Abstract

This work deals with buoyant tracers floating at the ocean surface, where the geostrophic velocity component is two dimensional and rotational (nondivergent) and the ageostrophic component can contain rotational and potential (divergent) contributions that are comparable in size. 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 long-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 analyze 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 analysis we consider ensembles of Lagrangian particles and introduce and apply the statistical topography methodology.

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  • Received 25 June 2019
  • Revised 19 October 2019

DOI:https://doi.org/10.1103/PhysRevE.100.063108

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Konstantin V. Koshel* and Dmitry V. Stepanov

  • V.I. Il'ichev Pacific Oceanological Institute, FEB RAS, Vladivostok 690041, Russia

Eugene A. Ryzhov and Pavel Berloff§

  • Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom

V. I. Klyatskin

  • A.M. Obukhov Atmospheric Physics Institute, RAS, Moscow 119017, Russia

  • *kvkoshel@poi.dvo.ru
  • step-nov@poi.dvo.ru
  • Also at V.I. Il'ichev Pacific Oceanological Institute, FEB RAS, Vladivostok 690041, Russia; ryzhovea@gmail.com
  • §p.berloff@imperial.ac.uk
  • klyatskin@yandex.ru

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Issue

Vol. 100, Iss. 6 — December 2019

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