Clustering of floating tracers in weakly divergent velocity fields
File(s)
Accepted version
Author(s)
Berloff, Pavel
Type
Journal Article
Abstract
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.
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.
Date Issued
2019-12-20
Date Acceptance
2019-12-05
Citation
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2019, 100, pp.1-15
ISSN
1539-3755
Publisher
American Physical Society
Start Page
1
End Page
15
Journal / Book Title
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
Volume
100
Copyright Statement
©2019 American Physical Society
Sponsor
Natural Environment Research Council (NERC)
The Leverhulme Trust
Natural Environment Research Council (NERC)
Identifier
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.063108
Grant Number
NE/R011567/1
RPG-2019-024
NE/T002220/1
Subjects
Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics, Mathematical
Physics
PASSIVE TRACERS
SURFACE
TURBULENCE
DIFFUSION
PARTICLES
TRANSPORT
VORTEX
GULF
FLOW
INTERMITTENCY
physics.flu-dyn
physics.flu-dyn
cond-mat.soft
76-XX, 65Cxx
Publication Status
Published
Article Number
063108
Date Publish Online
2019-12-20