Imperial College London
Alternate

ProfessorPavelBerloff

Faculty of Natural Sciences, Department of Mathematics

Professor in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 9662p.berloff Website

 
 
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Location

 

745Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Haigh:2022:10.1017/jfm.2022.126,
author = {Haigh, M and Berloff, P},
doi = {10.1017/jfm.2022.126},
journal = {Journal of Fluid Mechanics},
pages = {1--11},
title = {On the stability of tracer simulations with opposite-signed diffusivities},
url = {http://dx.doi.org/10.1017/jfm.2022.126},
volume = {937},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Haigh,M
AU  - Berloff,P
DO  - 10.1017/jfm.2022.126
EP  - 11
PY  - 2022///
SN  - 0022-1120
SP  - 1
TI  - On the stability of tracer simulations with opposite-signed diffusivities
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2022.126
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000761776800001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/on-the-stability-of-tracer-simulations-with-oppositesigned-diffusivities/F9EF46A74347A7092AB897341DA6ED19
UR  - http://hdl.handle.net/10044/1/96109
VL  - 937
ER  -
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