Hydrodynamic Stability and Turbulence (1922–1948)

An Annotation
  • S. Chandrasekhar
Part of the Werner Heisenberg Gesammelte Werke Collected Works book series (HEISENBERG, volume A / 1)


Heisenberg’s long paper (No. 2, p. 31 *), devoted in part to a study of the stability of plane-parallel laminar flows, is, by any standards, an important and fundamental contribution to the subject. In this paper, besides describing the essential steps that must be taken to solve the underlying mathematical problem, Heisenberg devises for the first time the use of “inner” and “outer” approximations with suitable matching conditions for the solution of ordinary differential equations (of order two or higher) with a turning point — a method later to be described by the initials “W.K.B.”. And beneath the mathematical developments, one can discern the operation of a powerful physical insight. Heisenberg himself described later the physical and the mathematical ideas in this early work of his in an address to the International Congress of Mathematicians in 1950 [1]. Perhaps a somewhat more technical account of these ideas may be useful as an introduction to his paper.


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  1. 1.
    W. Heisenberg: “On the Stability of Laminar Flow”, in Proc. Int. Congress of Mathematicians, Cambridge, Massachusetts, U.S.A., August 30-September 6, 1950, Volume II (American Mathematical Society, Providence, R.I., 1952) pp. 292–296 (reprinted as No. 36 in Volume B of Collected Works)Google Scholar
  2. 2.
    L. Hopf: Der Verlauf kleiner Schwingungen auf einer Strömung reibender Flüssigkeit. Ann. Phys. (4) 44, 1 – 60 (1914)CrossRefGoogle Scholar
  3. 3.
    C. C. Lin: On the stability of two-dimensional parallel flows. Parts I, II, III, Q. Appl. Math. 3, 117–142, 218–234, 277–301 (1945/46)Google Scholar
  4. 4.
    P. G. Drazin, W. H. Reid: Hydrodynamic Stability (Cambridge University Press, Cambridge 1981) pp. 124–251 (Chapter IV)Google Scholar
  5. 5.
    D. Meksyn, J. T. Stuart: Stability of viscous motion between parallel planes for finite disturbances. Proc. Roy. Soc. (London) A 208, 517 – 526 (1951)MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. 6.
    T. Herbert: Zur nichtlinearen Stabilitat ebener Potentialstromungen. Z. Angew. Math. Mech. 57, T187 – T189 (1977)CrossRefGoogle Scholar
  7. 7.
    S. Chandrasekhar: On Heisenberg’s elementary theory of turbulence. Proc. Roy. Soc. (London) A 200, 20 – 33 (1949)MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    G. K. Batchelor: The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge 1953) pp. 161–168 (7.5)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • S. Chandrasekhar
    • 1
  1. 1.ChicagoUSA

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