On the stability of tracer simulations with opposite-signed diffusivities
File(s)tracerFinal.pdf (712.57 KB)
Accepted version
Author(s)
Haigh, M
Berloff, P
Type
Journal Article
Abstract
Many recent studies have diagnosed opposite-signed diffusion eigenvalues to be a prevalent feature of the transfer tensor for diffusive tracer transport by oceanic mesoscale eddies. This diagnosed tensor, which we refer to as the diffusion tensor, therefore accounts for tracer filamentation effects. The preferential orientation of this filamentation is quantified by the principal axis of the diffusion tensor, namely the diffusion axis. Parameterisations of eddy diffusion commonly invoke a diffusion tensor, typically one with non-negative eigenvalues to avoid numerical issues. Motivated by the need to parameterise tracer filamentation, in this study we examine diffusion of a Gaussian tracer patch with imposed opposite-signed diffusion eigenvalues, and in particular we focus on the time scale for the onset of instability. For a fixed diffusion axis, numerical instability is an inevitable consequence of persistent up-gradient fluxes associated with the negative eigenvalue. For typical oceanic scales and diffusion magnitudes, this time scale is of the order of 100 days, but is shorter for larger negative eigenvalues or for finer grid resolutions. We show that imposing a time-dependent diffusion axis can lead to simulations with no onset of instability after 100 000 days of tracer evolution. Although motivated by oceanographic fluid dynamics, our results have much broader applications since diffusive processes are present in a wide range of fluid flows.
Date Issued
2022-02-28
Date Acceptance
2022-02-01
ISSN
0022-1120
Publisher
Cambridge University Press
Start Page
1
End Page
11
Journal / Book Title
Journal of Fluid Mechanics
Volume
937
Copyright Statement
© The Author(s), 2022. Published by Cambridge University Press. This article has been published in a revised form in Journal of Fluid Mechanics https://doi.org/10.1017/jfm.2022.126. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works.
Sponsor
Natural Environment Research Council (NERC)
The Leverhulme Trust
Natural Environment Research Council (NERC)
Identifier
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/on-the-stability-of-tracer-simulations-with-oppositesigned-diffusivities/F9EF46A74347A7092AB897341DA6ED19
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000761776800001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
NE/R011567/1
RPG-2019-024
NE/T002220/1
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
ocean processes
turbulent mixing
EDDY DIFFUSIVITY
PART I
TRANSPORT
DISSIPATION
DISPERSION
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
ocean processes
turbulent mixing
EDDY DIFFUSIVITY
PART I
TRANSPORT
DISSIPATION
DISPERSION
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status
Published
Article Number
ARTN R3
Date Publish Online
2022-02-28