Numerical Simulation of Turbulent Flows

  • S. A. Orszag


Digital computers capable of 1–10 MIPS (millions of instructions per second) are now readily available (e.g., CDC 6600,7600, IBM 360-195), while it is hoped that machines currently being developed will be capable of 10–100 MIPS (CDC STAR, Illiac, TI ASC, Cray Research). The great power of these machines has made possible the solution of some of the most challenging fluid dynamical problems, those of turbulence, by numerical solution of the Navier-Stokes equations.


Reynolds Number Eddy Viscosity Inertial Range Outflow Boundary Homogeneous Turbulence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Orszag, S. A., and Patterson, G. S., Numerical simulation of three-dimensional homogeneous isotropic turbulence, Phys. Rev. Lett. 28, 76–79 (1972).CrossRefGoogle Scholar
  2. 2.
    Orszag, S. A., On the resolution requirements of finite difference schemes, Stud. Appl. Math. 50, 395–397 (1971).MathSciNetMATHGoogle Scholar
  3. 3.
    Orszag, S. A., and Israeli, M., Numerical simulation of viscous incompressible flows, in: Aifhual Review of Fluid Mechanics, Vol. 6 ( M. Van Dyke, W. G. Vincenti, and J. V. Wehausen, eds.), Annual Reviews, Inc., Palo Alto, California (1974), pp. 281–318.Google Scholar
  4. 4.
    Kreiss, H. O., and Oliger, J., Methods for the Approximate Solution of Time Dependent Problems, Monograph Number 10, GARP Publ. Service, World Meteorology Organization (1973).Google Scholar
  5. 5.
    Herring, J. R., Orszag, S. A., Kraichnan, R. H., and Fox, D. G., Decay of two-dimensional homogeneous turbulence, /. Fluid Mech. 66, 417–444 (1974).MATHCrossRefGoogle Scholar
  6. 6.
    Orszag, S. A., and Pao, Y-H., Numerical computation of turbulent shear flows, in: Advances in Geophysics, Vol. 18A ( F. N. Frenkiel and R. E. Munn, eds.), Academic Press, New York (1974), pp. 225–236.Google Scholar
  7. 7.
    Grant, H. L., Stewart, R. W., and Moilliet, A., Turbulence spectra from a tidal channel, J. Fluid Mech. 12, 241–268 (1962).MATHCrossRefGoogle Scholar
  8. 8.
    Batchelor, G. K., The Theory of Homogeneous Turbulence, Cambridge University Press, Cambridge (1953).MATHGoogle Scholar
  9. 9.
    Orszag, S. A., Lectures on the statistical theory of turbulence, in: Fluid Dynamics ( R. Balian and J.-L. Peube, eds.), Gordon and Breach, New York (1977).Google Scholar
  10. 10.
    Grosch, C. E., and Orszag, S. A., Numerical solution of problems in unbounded regions: Coordinate transforms, J. Comp. Phys., to appear (1977).Google Scholar
  11. 11.
    Deardorff, J. W., A numerical study of three-dimensional turbulent channel flow at large Reynolds number, J. Fluid Mech. 41, 453–480 (1970).MATHCrossRefGoogle Scholar
  12. 12.
    Taylor, G. I., and Green, A. E., Mechanism of the production of small eddies from large ones, Proc. R. Soc. London, A, 158, 499–521 (1937).MATHCrossRefGoogle Scholar
  13. 13.
    Orszag, S. A., Numerical simulation of the Taylor-Green vortex, Computing Methods in Applied Science and Engineering Proceedings of the International Symposium, Pt. 2, Versailles, France, Springer, Berlin (1974), pp. 50–64.Google Scholar
  14. 14.
    Kraichnan, R. H., Inertial ranges in two-dimensional turbulence, Phys. Fluids 10, 1417–1423 (1967).CrossRefGoogle Scholar
  15. 15.
    Saffman, P. G., On the spectrum and decay of random two-dimensional vorticity distributions at large Reynolds number, Stud. Appl. Math. 50, 377–383 (1971).MATHGoogle Scholar
  16. 16.
    Kraichnan, R. H., An almost Markovian Galilean invariant turbulence model, J. Fluid Mech. 47, 513–524 (1971).MATHCrossRefGoogle Scholar
  17. 17.
    Kraichnan, R. H., The structure of isotropic turbulence at very high Reynolds numbers, J. Fluid Mech. 5, 497–543 (1959).MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Leith, C. E., Atmospheric predictability and two-dimensional turbulence, J. Atmos. Sci. 28, 145–161 (1971).CrossRefGoogle Scholar
  19. 19.
    Prandtl, L., Bericht tiber Untersuchungen zur ausgebildeten Turbulenz, Z. Angew. Math. Mech. 5, 136–139 (1925).MATHGoogle Scholar
  20. 20.
    Herring, J. R., Statistical theory of thermal convection at large Prandtl numbers, Phys. Fluids 12, 39–52 (1969).MATHCrossRefGoogle Scholar
  21. 21.
    Launder, B., and Spalding, D. B., Lectures in Mathematical Models of Turbulence, Academic Press, New York (1972).MATHGoogle Scholar
  22. 22.
    Harlow, F. H. (ed.), Turbulence Transport Modeling, American Institute of Aeronautics and Astronautics, New York (1973).Google Scholar
  23. 23.
    Deardorfï, J. W., A three-dimensional numerical investigation of the idealized planetary boundary layer, Geophys. Fluid Dyn. 1, 377–410 (1970).CrossRefGoogle Scholar
  24. 24.
    Smagorinsky, J., Manabe, S., and Holloway, J. L., Numerical results from a nine-level general circulation model of the atmosphere, Mon. Weather Rev. 93, 727–768 (1965).CrossRefGoogle Scholar
  25. 25.
    Kraichnan, R. H., Isotropic turbulence and inertial range structure, Phys. Fluids 9, 1728–1752 (1966).MATHCrossRefGoogle Scholar
  26. 26.
    Patterson, G. S., and Orszag, S. A., Numerical simulation of turbulence, Atmos. Technol. 3, 71–78 (1973).Google Scholar
  27. 27.
    Arakawa, A., Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow Part 1, /. Comput. Phys. 1, 119–143 (1966).MATHCrossRefGoogle Scholar
  28. 28.
    Orszag, S. A., Fourier series on spheres, Mon. Weather Rev. 102, 56–75 (1974).CrossRefGoogle Scholar
  29. 29.
    Gottlieb, D., and Orszag, S. A., Numerical Analysis of Spectral Methods, SIAM Monograph, Philadelphia (1977).MATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • S. A. Orszag
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations