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The evolution of wave correlations in uniformly turbulent, weakly non-linear systems

Published online by Cambridge University Press:  13 March 2009

Ronald C. Davidson
Ronald C. Davidson
Affiliation:
Department of Physics, University of California, Berkeley, California
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Abstract

A formalism is developed describing the time evolution of wave correlations in a uniformly turbulent ensemble of weakly non-linear systems. The statistics are built into the formalism a priori. With closure (of the hierarchy of equations for wave correlations) appropriate to the inclusion of resonant three-wave interactions, a (non-linear) kinetic equation for the two-wave correlations is derived and various properties of this equation are discussed. The effects of both bilinear and trilinear non-linearities are considered. Modifications of the formalism in situations where there is a weak (linear) instability γк, (γк/ωк ≪ 1) are also considered.

Type
Research Article
Information
Journal of Plasma Physics , Volume 1 , Issue 3 , August 1967 , pp. 341 - 359
Copyright
Copyright © Cambridge University Press 1967

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References

REFERENCES

Batchelor, G. K. 1956 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Benney, D. J. & Saffman, P. G. 1966 Proc. Roy. Soc. A 289, 301.Google Scholar
Davidson, R. C. 1966 Princeton University Plasma Physics Laboratory Report, Matt, 496, 56, 109.Google Scholar
Frieman, E. 1963 J. Math. Phys. 4, 410.CrossRefGoogle Scholar
Galeev, A. A. & Karpman, V. I. 1963 Soviet Phys. J.E.T.P. 17, 403.Google Scholar
Hasselmann, K. 1962 J. Fluid Mech. 12, 481.CrossRefGoogle Scholar
Hasselmann, K. 1963 J. Fluid Mech. 15, 273, 385.CrossRefGoogle Scholar
Iordanskii, S. V. & Kulikovskii, A. G. 1964 Soviet Phys. J.E.T.P. 19, 499.Google Scholar
Kadomstev, B. B. 1965 Plasma Turbulence. New York: Academic Press.Google Scholar
Kaufman, A. N. Private communication.Google Scholar
Lighthill, M. J. 1965 J. Inst. Math. Applics 1, 1.CrossRefGoogle Scholar
Litvak, M. M. 1960 Avco Everett Research Rep. no. 92.Google Scholar
Papoulis, A. 1965 Probability, Random Variables and Stochastic Processes. McGraw-Hill.Google Scholar
Sandri, G. 1963 Ann. Phys. 24, 332, 380.CrossRefGoogle Scholar
Sandri, G. 1965 Il Nuovo Cimento, Series X, 36, 67.CrossRefGoogle Scholar
Zabusky, N. J. & Kruskal, M. D. 1965 Phys. Rev. Lett. 15, 240.CrossRefGoogle Scholar