Turbulent, mixing of a scalar quantity in a 2-d mixing layer using matched asymptotic expansions

In this note analytical solutions for the turbulent mixing of a scalar quantity (mass, temperature, etc.) for a 2-d, free shear flow are developed. Approximate, i.e. thin shear layer self-similar forms for mass, momentum and the scalar quantity are derived, linearized using Göertler’s [ZAMM 22 (1942...

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Bibliographic Details
Published inApplied mathematical modelling Vol. 27; no. 12; pp. 955 - 962
Main Author De Chant, Lawrence J.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2003
Subjects
Matched asymptotic expansion
Scalar transport
Self-similar
Turbulent mixing layer
Matched asymptotic expansion
Turbulent mixing layer
Scalar transport
Self-similar
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Summary:In this note analytical solutions for the turbulent mixing of a scalar quantity (mass, temperature, etc.) for a 2-d, free shear flow are developed. Approximate, i.e. thin shear layer self-similar forms for mass, momentum and the scalar quantity are derived, linearized using Göertler’s [ZAMM 22 (1942) 244] perturbation argument and examined. Though successful for the mean velocity field, the regular expansion yields inconsistent solutions for the transport of a scalar. Sources of the non-uniformity are identified and a consistent result is obtained using matched asymptotic expansions. This result explains the success of semi-empirical convective velocity closures used by several researchers for a turbulence length scale equation.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0307-904X
DOI:10.1016/j.apm.2003.08.001