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The return to isotropy of homogeneous turbulence

Published online by Cambridge University Press:  12 April 2006

John L. Lumley  and
Gary R. Newman
John L. Lumley
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University, University Park Present address: Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853.
Gary R. Newman
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University, University Park Present address: Mechanical Engineering Department, Southeastern Massachusetts University, North Dartmouth, Massachusetts 02747.
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Abstract

The return to isotropy of homogeneous turbulence without mean velocity gradients is attacked by considering changes to be slow relative to turbulence time scales. This single assumption permits the problem to be cast as one of finding the form of three invariant functions. Examination of limiting behaviour for large Reynolds number and small anisotropy, as well as small Reynolds number and arbitrary anisotropy, places restrictions on the form of the functions. Realizability conditions (requiring that energies be non-negative) reduce the problem to two functions subject to further restrictions. A convenient interpolation form is found for the functions, satisfying all the restrictions, and it is shown that predictions based on this are in excellent agreement with all available data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 1 , 19 August 1977 , pp. 161 - 178
Copyright
© 1977 Cambridge University Press

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References

Batchelor, G. K. 1956 The Theory of Homogeneous Turbulence. Cambridge University Press.
Coleman, B. D. & Noll, W. 1961 Recent results in the continuum theory of viscoelastic fluids. Ann. N. Y. Acad. Sci. 89, 672–714.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, 657–682.Google Scholar
Kolmogorov, A. N. 1941 Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Lumley, J. L. 1970a Toward a turbulent constitutive relation. J. Fluid Mech. 41, 413–434.Google Scholar
Lumley, J. L. 1970b Stochastic Tools in Turbulence. Academic Press.
Lumley, J. L. 1975 Prediction methods for turbulent flows, introduction. Lecture notes for series Prediction Methods for Turbulent Flows.Von Kármân Inst., Rhode-St-Genese, Belgium.
Lumley, J. L. & Khajeh-Nouri, B. 1972 Computational modeling of turbulent transport. Adv. in Geophys. A 18, 169–192.Google Scholar
Lumley, J. L., Zeman, O. & Siess, J. 1977 The influence of buoyancy on turbulent transport. J. Fluid Mech. (in press).
Mills, R. R. & Corrsin, S. 1959 Effects of contraction on turbulence and temperature fluctuations generated by a warm grid. N.A.S.A. Memo. no. 5-5-59W.Google Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. M.I.T. Press.
Orszag, S. A. & Patterson, G. S. 1972 Numerical simulation of turbulence. Statistical Models and Turbulence, pp. 127–147. Lecture Notes in Physics, vol. 12. Springer.
Reynolds, W. C. 1974 Computation of turbulent flows. 7th Fluid Plasma Dyn. Cong. A.I.A.A. Paper no. 74–556.
Reynolds, W. C. 1976 Computation of turbulent flows. Ann. Rev. Fluid Mech. 8, 183–208.Google Scholar
Rotta, J. 1951 Statistische Theorie nichthomogener Turbulenz. Z. Phys. 129, 547–572.Google Scholar
Schumann, U. 1977 Realizability of Reynolds stress turbulence models. To be submitted to Phys. Fluids.Google Scholar
Schumann, U. & Herring, J. R. 1976 Axisymmetric homogeneous turbulence: a comparison of direct spectral simulations with the direct-interaction approximation. J. Fluid Mech. 76, 755–782.Google Scholar
Schumann, U. & Patterson, G. S. 1977 Numerical study of the return of axisymmetric turbulence to isotropy. Submitted to J. Fluid Mech.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. M.I.T. Press.
Uberoi, M. S. 1956 Effect of wind tunnel contraction on free stream turbulence. J. Aero. Sci. 23, 754–764.Google Scholar
Uberoi, M. S. 1957 Equipartition of energy and local isotropy in turbulent flows. J. Appl. Phys. 28, 1265–1170.Google Scholar
Volterra, V. 1959 Theory of Functionals and of Integral and Integro-differential Equations. Dover.
Zeman, O. 1975 The dynamics of entrainment in the planetary boundary layer: a study in turbulence modeling and parameterization. Ph.D. thesis, The Pennsylvania State University.