On eddy transport in the ocean. Part I: The diffusion tensor
File(s)
Accepted version
Author(s)
Haigh, Michael
Sun, Luolin
McWilliams, James C
Berloff, Pavel
Type
Journal Article
Abstract
This study provides an interpretation of isopycnal eddy transport for mass and passive tracers in double-gyre
eddy-resolving oceanic circulation. This paper focuses on a transport/diffusion tensor representation of the
eddy tracer flux, and a companion paper will focus on advective eddy-induced tracer and mass transports. We
use a spatial filter to separate the large and small scales, which leads to results distinct from those obtained via
a temporal Reynolds eddy decomposition. To work towards a parameterisation, we relate the eddy tracer flux
to the large-scale tracer gradient via the transport tensor 𝑲. The symmetric part of 𝑲 is the diffusion tensor,
𝑺, which parameterises diffusive fluxes and whose mixing properties are determined by the signs of its eigenvalues. The eigenvalues of 𝑺 are robustly of opposite sign (polar) and thus quantify filamentation of the tracer
via both up- and down-gradient fluxes. Given the prevalence of polar eigenvalues – which are also obtained for
Reynolds eddy fluxes – representing their associated effects should be a target of future eddy tracer transport
closures. Given the inherent inhomogeneity and anisotropy of the eddy-induced transport, we argue that a full
transport tensor is better suited to this task than scalar coefficients or diagonal tensors. The diffusion axis,
which represents the direction of preferential mixing, tends to align with the large-scale velocity vector and
contours of large-scale relative vorticity and layer thickness. Strong shears can inhibit this alignment. We show
that the large-scale velocity gradient matrix may be suitable for parameterising the transport tensor, in particular at depth. Furthermore, since entries of 𝑲 and 𝑺 exhibit probabilistic distributions when conditioned on certain large-scale flow features, we suggest that a stochastic closure for the eddy transport would be most suitable.
eddy-resolving oceanic circulation. This paper focuses on a transport/diffusion tensor representation of the
eddy tracer flux, and a companion paper will focus on advective eddy-induced tracer and mass transports. We
use a spatial filter to separate the large and small scales, which leads to results distinct from those obtained via
a temporal Reynolds eddy decomposition. To work towards a parameterisation, we relate the eddy tracer flux
to the large-scale tracer gradient via the transport tensor 𝑲. The symmetric part of 𝑲 is the diffusion tensor,
𝑺, which parameterises diffusive fluxes and whose mixing properties are determined by the signs of its eigenvalues. The eigenvalues of 𝑺 are robustly of opposite sign (polar) and thus quantify filamentation of the tracer
via both up- and down-gradient fluxes. Given the prevalence of polar eigenvalues – which are also obtained for
Reynolds eddy fluxes – representing their associated effects should be a target of future eddy tracer transport
closures. Given the inherent inhomogeneity and anisotropy of the eddy-induced transport, we argue that a full
transport tensor is better suited to this task than scalar coefficients or diagonal tensors. The diffusion axis,
which represents the direction of preferential mixing, tends to align with the large-scale velocity vector and
contours of large-scale relative vorticity and layer thickness. Strong shears can inhibit this alignment. We show
that the large-scale velocity gradient matrix may be suitable for parameterising the transport tensor, in particular at depth. Furthermore, since entries of 𝑲 and 𝑺 exhibit probabilistic distributions when conditioned on certain large-scale flow features, we suggest that a stochastic closure for the eddy transport would be most suitable.
Date Issued
2021-08-01
Date Acceptance
2021-06-01
Citation
Ocean Modelling, 2021, 164, pp.1-15
ISSN
1463-5003
Publisher
Elsevier
Start Page
1
End Page
15
Journal / Book Title
Ocean Modelling
Volume
164
Copyright Statement
© 2021 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Natural Environment Research Council (NERC)
The Leverhulme Trust
Natural Environment Research Council (NERC)
Natural Environment Research Council (NERC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000671436200001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
NE/R011567/1
RPG-2019-024
NE/T002220/1
EP/V520354/1
Subjects
Science & Technology
Physical Sciences
Meteorology & Atmospheric Sciences
Oceanography
Eddy transport
Eddy diffusion
Tracer parameterisations
TRACER
DISPERSION
EDDIES
SUPPRESSION
PATTERNS
FLUXES
MODEL
JETS
Publication Status
Published
Article Number
ARTN 101831
Date Publish Online
2021-06-07