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TECHNICAL PAPERS

On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence

[+] Author and Article Information
J. Jovanović, I. Otić

Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058, Germany

J. Fluids Eng 122(1), 48-50 (Dec 08, 1999) (3 pages) doi:10.1115/1.483225 History: Received June 08, 1999; Revised December 08, 1999
Copyright © 2000 by ASME
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References

Prandtl, L., 1931, “On the Role of Turbulence in Technical Hydrodynamics,” Proceedings of the World Engineering Congress, Tokyo, 6 , pp. 495–507.
Kolmogorov,  A. N., 1942, “Equations of Motion of an Incompressible Turbulent Fluid,” Izvestiya Akad. Nauk SSSR, Ser., 6, pp. 56–58.
Spalding,  D. B., 1991, “Kolmogorov’s Two-Equation Model of Turbulence,” Proc. R. Soc. London, Ser. A, 434, pp. 211–216.
Boussinesq,  J., 1877, “Theorie de l’écoulement Tourbillant,” Acad. Sci., Paris, 23, pp. 56–58.
Spalding, D. B., and Launder, D. B., 1971, Mathematical Models and Turbulence, Mechanical Engineering Department, Imperial College, London.
Saffman,  P. G., 1974, “Model Equations for Turbulent Shear Flow,” Studies Appl. Math., 53, p. 17.
Pope,  S. B., 1975, “A More General Effective Viscosity Hypothesis,” J. Fluid Mech., 72, pp. 331–340.
Speziale,  C. G., 1987, “On Nonlinear k−L and k−ε Models of Turbulence,” J. Fluid Mech., 178, pp. 459–475.
Lumley,  J. L., 1978, “Computational Modeling of Turbulent Flows,” Adv. Appl. Mech., 18, pp. 123–176.
Rotta, J. C., 1972, Turbulente Strömungen: Eine Einführung in die Theorie and ihre Anwendung, B. G. Teubner, Stuttgart, pp. 120–127.
Rogallo, R. S., 1981, “Numerical Experiments in Homogeneous Turbulence,” NASA Technical Memorandum 81315.
Lee, M. J., 1985, “Numerical Experiments on the Structure of Homogeneous Turbulence,” Ph.D. thesis, Stanford University.

Figures

Grahic Jump Location
Anisotropy invariant map and values of the effective viscosity for the limiting states of turbulence
Grahic Jump Location
A cross plot of aij versus −II1/2Sij/S for axisymmetric strained turbulence from direct numerical simulations: Rogallo 11, Lee 12

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