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The spectra of turbulence in a compressible fluid; eddy turbulence and random noise

Published online by Cambridge University Press:  24 October 2008

J. E. Moyal
J. E. Moyal
Affiliation:
University of Manchester
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Abstract

The state of a real fluid is completely specified by its velocity, density, pressure and temperature fields. When the fluid is in turbulent flow, all these quantities fluctuate in a disordered manner. The method of space Fourier spectra is used to show that these field variables separate into two physically distinct groups, one corresponding to fluctuating acoustical waves, or random noise, and the other to fluctuating vorticity, or eddy turbulence. The corresponding decomposition of the spectral and correlation tensors in a homogeneous field of turbulence is given. The noise Fourier components are shown to be coupled to the eddy Fourier components only through the non-linear inertia terms in the dynamical equations of the fluid; whereas the former propagate as acoustical waves, the wave character of the latter is due entirely to the mean motion of the fluid. The measurement of the noise component, its attenuation through absorption by walls and its effects on the eddy component are discussed. Finally, the dynamical equations for the eddy component of the velocity spectral tensor in a homogeneous field of turbulence are compared with the corresponding equations for an incompressible fluid.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 2 , April 1952 , pp. 329 - 344
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

(1)Ackeret, J. Gasdynamik. Handbuch der Physih, vol. 7 (Berlin, 1927), p. 289.Google Scholar
(2)Bass, J.C.R. Acad. Sci., Paris, 228 (1948), 228.Google Scholar
(3)Bass, J. and Agostini, L.Les théories de la turbulence (Paris, 1950).Google Scholar
(4)Batchelor, G. K.Proc. seventh int. Congr. appl. Mech., 1948, Introduction, p. 27.Google Scholar
(5)Batchelor, G. K.Proc. roy. Soc. A, 195 (1949), 513.Google Scholar
(6)Batchelor, G. K. and Townsend, A. A.Proc. roy. Soc. A, 194 (1948), 527.Google Scholar
(7)Heisenberg, W.Z. Phys. 124 (1948), 628.CrossRefGoogle Scholar
(8)Kampé de Fériet, J.Proc. seventh int. Congr. appl. Mech., 1948, Introduction, p. 6.Google Scholar
(9)Kármán, T. de and Howarth, L.Proc. roy. Soc. A, 164 (1938), 192.Google Scholar
(10)Lévy, P.Processus stochastiques (Paris, 1948).Google Scholar
(11)Lighthill, M. J.Proc. roy. Soc. A (in the Press).Google Scholar
(12)Morse, P. M.Vibration and sound, 2nd ed. (New York, 1948), pp. 382–429.Google Scholar
(13)Moyal, J. E.J.R. statist. Soc. B, 11 (1949), 150.Google Scholar
(14)Rayleigh, J. W. S.The theory of sound, vol. 2 (London, 1896), pp. 415–31.Google Scholar
(15)Robertson, R.Proc. Camb. phil. Soc. 36 (1940), 209.CrossRefGoogle Scholar