Advertisement

The statistical problem of turbulence

  • Ekkehart Kröner
Part of the International Centre for Mechanical Sciences book series (CISM, volume 92)

Abstract

This is the classical example of an application of statistical and probability theory in continuum mechanics. The stochastic nature of the turbulent flow follows from the fact that the particle velocities fluctuate over distances which are small compared to other dimensions of the flow. The question whether turbulent flow is a solution of the Navier-Stokes equations has been discussed and is not trivial. Today it seems to be generally accepted that the Navier-Stokes equations should, in fact, allow turbulent flow.

Keywords

Fourier Space Ordinary Space Kinetic Energy Density Small Eddy Divergency Condition 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Batchelor, The Theory of Homogeneous Turbulence, Cambridge University Press, London —New York 1953MATHGoogle Scholar
  2. M.J. Beran, Statistical Continuum Theories, Interscience Publishers, New York 1968MATHGoogle Scholar
  3. H. Goering, Sammelband zur Statistischen Theorie der Turbulenz, Berlin 1958Google Scholar
  4. G.I. Taylor, Proc. London Math. Soc. 20, 196 (1921)MATHGoogle Scholar
  5. A.A. Friedmann and L.W. Keller, Proc. Int. Congr. Appl. Mech. Delft 1924Google Scholar
  6. G.I. Taylor, Proc. Roy. Soc. (London) A 151, 421 (1935) and A 156, 307 (1936)Google Scholar
  7. T. von Karman, Proc. Nat. Acad. Sci. U.S. 23, 98 (1937) and J. Aeron. Sci. 4, 131 (1937)CrossRefMATHGoogle Scholar
  8. T. von Karman and L. Howarth, Proc. Roy. Soc. (London) A 164, 192 (1938)Google Scholar
  9. A.A. Kolmogorov, Compt. Rend. Acad. Sci. URSS 30, 301 (1941); Engl. Transl. in “Turbulence”, S. Friedlander and L. Topper Eds., Interscience Publishers, New YorkGoogle Scholar
  10. C.F. von Weizsticker, Z. Physik 124, 614 (1948)CrossRefMathSciNetGoogle Scholar
  11. W. Heisenberg, Z. Physik 124, 628 (1948)CrossRefMATHMathSciNetGoogle Scholar
  12. W. Heisenberg, Proc. Roy. Soc. (London) A 195, (1948/49)Google Scholar
  13. E. Hopf, J. Ratl. Mech. Anal. 1, 87 (1952)MATHGoogle Scholar
  14. E. Hopf, Proc. Symp. Appl. Math. 13, 165 (1962), Am. Math. Soc., Providence, R.I. These papers refer to the functional formulation of the theory of turbulence.Google Scholar
  15. H. Wyld, Ann. of Phys. 14, 143 (1961)CrossRefMATHMathSciNetGoogle Scholar
  16. V. Tatarski, Wave Propagation in a Turbulent Medium, McGraw Hill, New York 1961MATHGoogle Scholar
  17. S. Edwards, J. Fluid Mech. 18, 239 (1964)CrossRefMathSciNetGoogle Scholar
  18. R. Deissler, Phys. Fluids 8, 291, 2106 (1965)CrossRefMathSciNetGoogle Scholar
  19. R. Kraichnan, Phys. Fluids 1, 358, 1728 (1966)Google Scholar
  20. L.S.G. Kovasznay, Turbulence Measurement in Applied Mechanics Surveys, H.N. Abramson. H. Liebowitz, J.M. Crowley, S. Juhasz Eds., Spartan Books, Macmillan and Co. Ltd., Washington, D.C. 1966 (describes experimental technics).Google Scholar

Copyright information

© Springer-Verlag Wien 1971

Authors and Affiliations

  • Ekkehart Kröner
    • 1
  1. 1.University of StuttgartGermany

Personalised recommendations