Asymptotic theory of turbulent shear flows

Yajnik, Kirit S. (1970) Asymptotic theory of turbulent shear flows Journal of Fluid Mechanics, 42 (2). pp. 411-427. ISSN 0022-1120

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A theory is proposed in this paper to describe the behaviour of a class of turbulent shear flows as the Reynolds number approaches infinity. A detailed analysis is given for simple representative members of this class, such as fully developed channel and pipe flows and two-dimensional turbulent boundary layers. The theory considers an underdetermined system of equations and depends critically on the idea that these flows consist of two rather different types of regions. The method of matched asymptotic expansions is employed together with asymptotic hypotheses describing the order of various terms in the equations of mean motion and turbulent kinetic energy. As these hypotheses are not closure hypotheses, they do not impose any functional relationship between quantities determined by the mean velocity field and those determined by the Reynolds stress field. The theory leads to asymptotic laws corresponding to the law of the wall, the logarithmic law, the velocity defect law, and the law of the wake.

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
ID Code:60650
Deposited On:09 Sep 2011 09:44
Last Modified:09 Sep 2011 09:44

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