Effective diffusion of scalar fields in a chaotic flow

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Effective diffusion of scalar fields in a chaotic flow

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dc.contributor.author Turner, M. R. en_GB
dc.contributor.author Gilbert, Andrew D. en_GB
dc.contributor.author Thuburn, John en_GB
dc.contributor.department University of Exeter en_GB
dc.date.accessioned 2009-03-19T16:32:19Z en_GB
dc.date.accessioned 2011-01-25T10:33:32Z en_US
dc.date.accessioned 2013-03-20T12:27:00Z
dc.date.issued 2008 en_GB
dc.description.abstract The advection of a tracer field in a fluid flow can create complex scalar structures and increase the effect of weak diffusion by orders of magnitude. One tool to quantify this is to measure the flux of scalar across contour lines of constant scalar. This gives a diffusion equation in area coordinates with an effective diffusion that depends on the structure of the scalar field and, in particular, takes large values when scalar contours become very extended. The present paper studies the properties of this effective diffusion using a mixture of analytical and numerical tools. First the presence of hyperbolic stationary points, that is, saddles, in the scalar concentration field is investigated analytically, and it is shown that these give rise to singular spikes in the effective diffusion. This is confirmed in numerical simulations in which complex scalar fields are generated using a time-periodic flow. Issues of numerical resolution are discussed and results are given on the dependence of the effective diffusion on grid resolution and discretization in area or scalar values. These simulations show complex dependence of the effective diffusion on time as saddle points appear and disappear in the scalar field. It is found that time averaging (in the presence of an additional scalar source term) removes this dependence to leave robust results for the effective diffusion. en_GB
dc.identifier.citation 20 (10), article 107103 en_GB
dc.identifier.doi 10.1063/1.2998461 en_GB
dc.identifier.uri http://hdl.handle.net/10036/56441 en_GB
dc.language.iso en en_GB
dc.publisher American Institute of Physics en_GB
dc.relation.url http://dx.doi.org/10.1063/1.2998461 en_GB
dc.relation.url http://link.aip.org/link/?PHFLE6/20/107103/1 en_GB
dc.subject Chaos en_GB
dc.subject Diffusion en_GB
dc.subject Flow simulation en_GB
dc.subject Pulsatile flow en_GB
dc.title Effective diffusion of scalar fields in a chaotic flow en_GB
dc.type Article en_GB
dc.date.available 2009-03-19T16:32:19Z en_GB
dc.date.available 2011-01-25T10:33:32Z en_US
dc.date.available 2013-03-20T12:27:00Z
dc.identifier.issn 1070-6631 en_GB
dc.description Copyright © 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Fluids 20 (2008) and may be found at http://link.aip.org/link/?PHFLE6/20/107103/1 en_GB
dc.identifier.journal Physics of Fluids en_GB


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