On the Degeneration of Isotropic Turbulence in an Incompressible Viscous Fluid

  • V. M. Tikhomirov
Part of the Mathematics and Its Applications (Soviet Series) book series (MASS, volume 25)


As in [1, 2], we assume that the velocity components
$${{u}_{a}}(P,t) = {{u}_{a}}({{x}_{1}},{{x}_{2}},{{x}_{3}},t)$$
at the point P = (x 1 ,x 2 , x3) at time t are random variables and denote by Ā the mathematical expectation of a random variable A.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.D. Millionshchikov, ‘Degeneration of homogeneous isotropic turbulence in viscous incompressible fluids’, Dokl. Akad. Nauk SSSR 22:5 (1939), 236–240 (in Russian).Google Scholar
  2. 2.
    A.N. Kolmogorov, ‘Local structure of turbulence in an incompressible viscous fluid at very large Reynolds numbers’, Dokl. Akad. Nauk SSSR 30:4 (1941), 299–303 (in Russian). (See No. 45.)ADSGoogle Scholar
  3. 3.
    G.I. Taylor, ‘Statistical theory of turbulence’, I—IV, Proc. Roy. Soc. London A151 (1935), No. 874, 421–478.ADSGoogle Scholar
  4. 4.
    S. Goldstein, ed. Modern developments in fluid mechanics, Vol. 1, §91, Oxford Univ. Press, 1938.Google Scholar
  5. 5.
    Th. von Karman and L. Howarth, ‘On the statistical theory of isotropic turbulence’, Proc. Roy. Soc. London A164 (1938), No. 917, 192–245.ADSGoogle Scholar
  6. 6.
    L.G. Loitsyanskii, ‘Some basic regularities of an isotropic turbulent flow’, Trudy TsAG I440 (1939), 3–23.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • V. M. Tikhomirov

There are no affiliations available

Personalised recommendations