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A ν-fluid model of homogeneous turbulence subjected to uniform mean distortion

Published online by Cambridge University Press:  29 March 2006

J. M. Dowden
J. M. Dowden
Affiliation:
Department of Mathematics, University of Essex, Colchester, England
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Abstract

In two previous papers (Proudman 1970; Dowden 1972) it has been shown that some of the phenomena of turbulence a t high Reynolds numbers can be modelled by a suitable chosen member of the class of ν-fluids. These are non-Newtonian fluids all of whose properties depend only on a single dimensional constant whose dimensions are those of viscosity. The purpose of this paper is to construct an equation to model homogeneous turbulence in the presence of a spatially constant rate of deformation in the limit of infinite Reynolds number.

The equation employed is that of a doubly degenerate third-order v-fluid (in Proudman's classification) in the limit ν → 0. In such a fluid the stress tensor S is governed by an equation of the form \[ A\dot{S}\ddot{S}+B\dot{S}^2+Cu^{\prime}S\dot{S}+D\dot{u}^{\prime}S^2 + Eu^{\prime 2}S^2 = 0, \] where A, B,…, E are isotropic tensor constants of the fluid, u′ is the total rate of deformation tensor and dots denote time derivatives. A list of properties required of the equation and its solution is proposed, and the most general form of A, B,…, E is given consistent with these requirements. Computed solutions of this equation are compared with the results of experiments on homogeneous turbulence, and are found to agree well with them.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 63 , Issue 1 , 18 March 1974 , pp. 33 - 50
Copyright
© 1974 Cambridge University Press

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