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The scale effect in compressible turbulence

Published online by Cambridge University Press:  24 October 2008

D. G. Crighton
D. G. Crighton
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

The pressure fluctuations in a compressible fluid in statistically steady isotropic motion are studied. These depend crucially on the scale of the turbulent region. If the region is small enough, the mean square acoustic pressure varies as the linear scale of the region, and as the fourth power of the turbulence Mach number. In the limit of infinite scale, however, diffusive effects limit the otherwise infinite pressure fluctuations as first shown by Lighthill(6). The mean square acoustic pressure then varies as the Mach number and as the turbulence Reynolds number. The pressure fluctuations above a sheet composed of statistically uniformly fluctuating sources are also examined. Here the mean square pressure diverges, initially, in proportion to the logarithm of the scale of the sheet, until viscous effects again become significant in limiting the pressure.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 2 , March 1969 , pp. 557 - 566
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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