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The relaxation of stress in a ≠-fluid with reference to the decay of homogeneous turbulence

Published online by Cambridge University Press:  29 March 2006

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

It was suggested by Proudman (1970) that many of the phenomena of turbulence at high Reynolds number could be modelled by a suitably chosen member of a class of non-Newtonian fluids, ν-fluids, all of whose properties depend only on a single dimensional constant with the dimensions of viscosity. This paper investigates the relaxation of homogeneous stress in a doubly degenerate third-order ν-fluid (which is the simplest member of the class that can possibly be used to model turbulence) in the limit ν → 0.

The equation which governs the stress tensor S is of the form \[ AS\ddot{S} + B\dot{S}^2 = 0, \] where A and B are isotropic tensor constants of the fluid; its differential structure can be of four distinct types. A list of properties required of the solutions of the equation is set out, and it is shown that only one of the four types has all the properties demanded of it. The behaviour of solutions of this equation is found to be consistent with the theoretical and experimental results on the decay of homogeneous turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 56 , Issue 4 , 28 December 1972 , pp. 641 - 656
Copyright
© 1972 Cambridge University Press

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References

Batchelor, G. K. & Townsend, A. A. 1948 Decay of isotropic turbulence in the initial period. Proc. Roy. Soc. A 193, 539.Google Scholar
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25, 657.Google Scholar
Proudman, I. 1970 On the motion of ≠-fluids. J. Fluid Mech. 44, 563.Google Scholar
Townsend, A.A. 1951 The passage of turbulence through wire gauzes. Quart. J. Mech. Appl. Math. 4, 308.Google Scholar
Townsend, A. A. 1954 The uniform distortion of homogeneous turbulence. Quart. J. Mech. Appl. Math. 7, 104.Google Scholar
Tucker, H. J. & Reynolds, A. J. 1968 The distortion of turbulence by irrotational plane strain. J. Fluid Mech. 32, 657.Google Scholar
Uberoi, M. S. 1963 Energy transfer in isotropic turbulence. Phys. Fluids, 6, 1048.Google Scholar