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The mean value of the fluctuations in pressure and pressure gradient in a turbulent fluid

Published online by Cambridge University Press:  24 October 2008

A. E. Green
A. E. Green
Affiliation:
Jesus College
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Extract

1. Taylor has shown (1) that two characteristic lengthsλ and λη may be defined for turbulent fluid motion. The length λ, which is connected with the dissipation of energy, is, for isotropic turbulence, given by

where is the mean rate of dissipation of energy per unit volume and represents the mean square value of any component of velocity. The length λη can be defined in terms of thus

where For isotropic turbulence Taylor assumed that

where B is a constant. Since the turbulence is isotropic,

and so, from (1), (2), (3) and (4) we have

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 34 , Issue 4 , October 1938 , pp. 534 - 539
Copyright
Copyright © Cambridge Philosophical Society 1938

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References

REFERENCES

(1)Taylor, . Proc. Roy. Soc. A, 151 (1935), 421–78.Google Scholar
(2)Taylor, . Proc. Cambridge Phil. Soc. 32 (1936), 380–4.Google Scholar
(3)Kármán, and Howarth, . Proc. Roy. Soc. A, 164 (1938), 192–215.Google Scholar