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The invariant theory of isotropic turbulence

Published online by Cambridge University Press:  24 October 2008

H. P. Robertson
H. P. Robertson
Affiliation:
Princeton UniversityPrinceton, N.J.
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Extract

The statistical theory of isotropic turbulence, initiated by Taylor (3) and extended by de Kármán and Howarth (2), has proved of value in attacking problems associated with the decay of turbulence. In its application to such hydro-dynamical problems, the theory falls into two parts, a kinematical part and a dynamical part. The kinematical aspect consists in setting up correlations between velocity components, or their derivatives, at two arbitrary points in the fluid, and reducing the form of the tensor thus obtained in accordance with the severely restrictive assumption of isotropic turbulence; the success of de Kármán and Howarth's investigations is largely attributable to their improved treatment of this purely kinematical problem. The dynamical part then consists in applying the implications of the equations of continuity and motion to the functions defining the correlation tensors, in order to obtain information concerning their functional dependence on time and on the displacement between the two points for which the correlations are computed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 36 , Issue 2 , April 1940 , pp. 209 - 223
Copyright
Copyright © Cambridge Philosophical Society 1940

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References

REFERENCES

(1)Jeffreys, H.Cartesian tensors (Cambridge, 1931).Google Scholar
(2)de Kármán, T. and Howarth, L.Proc. Roy. Soc. A, 164 (1938), 192–215.Google Scholar
(3)Taylor, G. I.Proc. Roy. Soc. A, 151 (1935), 421–78.Google Scholar
(4)Taylor, G. I.Proc. Roy. Soc. A, 164 (1938), 476–90.Google Scholar
(5)Weitzenböck, R.Invariantentheorie (Groningen, 1923).Google Scholar