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The diffusive strip method for scalar mixing in two dimensions

Published online by Cambridge University Press:  06 September 2010

P. MEUNIER  and
E. VILLERMAUX
P. MEUNIER*
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE), CNRS, Aix-Marseille Université, 13384 Marseille Cedex 13, France
E. VILLERMAUX
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE), CNRS, Aix-Marseille Université, 13384 Marseille Cedex 13, France Institut Universitaire de France, 75005 Paris, France
*
†Email address for correspondence: meunier@irphe.univ-mrs.fr
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Abstract

We introduce a new numerical method for the study of scalar mixing in two-dimensional advection fields. The position of an advected material strip is computed kinematically, and the associated convection–diffusion problem is solved using the computed local stretching rate along the strip, assuming that the diffusing strip thickness is smaller than its local radius of curvature. This widely legitimate assumption reduces the numerical problem to the computation of a single variable along the strip, thus making the method extremely fast and applicable to any large Péclet number. The method is then used to document the mixing properties of a chaotic sine flow, for which we relate the global quantities (spectra, concentration probability distribution functions (PDFs), increments) to the distributed stretching of the strip convoluted by the flow, possibly overlapping with itself. The numerical results indicate that the PDF of the strip elongation is log normal, a signature of random multiplicative processes. This property leads to exact analytical predictions for the spectrum of the field and for the PDF of the scalar concentration of a solitary strip. The present simulations offer a unique way of discovering the interaction rule for building complex mixtures which are made of a random superposition of overlapping strips leading to concentration PDFs stable by self-convolution.

JFM classification

Mixing: Chaotic advection Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 662 , 10 November 2010 , pp. 134 - 172
Copyright
Copyright © Cambridge University Press 2010

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References

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