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A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers

Published online by Cambridge University Press:  29 March 2006

James W. Deardorff
National Center for Atmospheric Research, Boulder, Colorado 80302


The three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers. A total of 6720 uniform grid intervals were used, with sub-grid scale effects simulated with eddy coefficients proportional to the local velocity deformation. The agreement of calculated statistics against those measured by Laufer ranges from good to marginal. The eddy shapes are examined, and only the u-component, longitudinal eddies are found to be elongated in the downstream direction. However, the lateral v eddies have distinct downstream tilts. The turbulence energy balance is examined, including the separate effects of vertical diffusion of pressure and local kinetic energy.

It is concluded that the numerical approach to the problem of turbulence at large Reynolds numbers is already profitable, with increased accuracy to be expected with modest increase of numerical resolution.

Research Article
© 1970 Cambridge University Press

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Angell, J. K., Pack, D. H. & Dickinson, C. R. 1968 J. Atmos. Sci. 25, 707.
Arakawa, A. 1966 J. Computational Phys. 1, 119.
Aziz, K. & Hellums, J. D. 1967 Phys. Fluids, 10, 314.
Chorin, A. J. 1968 Math. Computation, 22, 745.
Comte-Bellot, G. 1965 Publ. Scientifiques et Techniques du Ministère de l'Air, no. 419.
Corrsin, S. 1961 American Scientist, 49, 300.
Deardorff, J. W. 1969 NCAR Manuscript 69–19. Boulder, Colorado.
Fischer, G. 1965 Mon. Weath. Rev. 93, 1.
Harlow, F. H. & Welch, J. E. 1965 Phys. Fluids, 8, 2182.
Hinze, J. O. 1959 Turbulence. New York: McGraw-Hill.
Kasahara, A. & Washington, W. M. 1967 Mon. Weath. Rev. 95. 7.
Laufer, J. 1950 NACA TN 1053.
Laufer, J. 1954 NACA TR 1174.
Leith, C. E. 1965 Methods in Computational Physics, 4. New York: Academic.
Leith, C. E. 1968 Proceedings of the WMO-IUGG Symposium on Numerical Weather Prediction, Tokyo, Nov. 1968. (To be published.)
Lilly, D. K. 1967 Proceedings of the IBM Scientific Computing Symposium on Environmental Sciences IBM Form no. 320–1951, 195.
Lumley, J. L. & Panofsky, H. A. 1964 Structure of Atmospheric Turbulence. Interscience.
Mintz, Y. 1965 W.M.O. TN 66, 141.
Orszag, S. A. 1969 Phya. Fluids, 12, II–250.
Reynolds, O. 1895 Phil. Trans. A 186, 123.
Smagorinsky, J., Manabe, S. & Holloway, J. L. 1965 Mon. Weath. Rev. 93, 727.
Taylor, G. I. 1938 Proc. Roy. Soc. A 164, 15.
Uberoi, M. S. 1954 NACA TN 3116.
Uberoi, M. S. 1963 Phys. Fluids, 6, 1048.