Effective diffusion of scalar fields in a chaotic flow

Turner, M.R., Gilbert, A.D. and Thuburn, J. (2008) Effective diffusion of scalar fields in a chaotic flow Physics of Fluids, 20 (10). ISSN 1089-7666

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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.

Item Type: Journal article
Additional Information: © The Author(s) and American Institute of Physics, 2008
Subjects: G000 Computing and Mathematical Sciences > G100 Mathematics
H000 Engineering
DOI (a stable link to the resource): 10.1063/1.2998461
Faculties: Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Engineering and Product Design Research > Automotive Engineering
Depositing User: Dr Matthew Turner
Date Deposited: 26 Nov 2009
Last Modified: 21 May 2014 11:01
URI: http://eprints.brighton.ac.uk/id/eprint/6465

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