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The irrotational motion outside a free turbulent boundary

Published online by Cambridge University Press:  24 October 2008

O. M. Phillips
O. M. Phillips
Affiliation:
Trinity CollegeCambridge
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Abstract

In this paper there is considered the irrotational motion of an infinite fluid when the normal velocity across a plane is specified as a stationary random function of position in the plane, and a solution is obtained in terms of the specified boundary conditions. It is shown that the mean square velocity normal to the plane is equal to the sum of the mean squares of the velocities in the other two orthogonal directions. The asymptotic variations with distance normal to the plane are found for functions representing the important properties of the motion, and, in particular, the energy of the fluctuations is shown to be inversely proportional to the fourth power of the distance from the plane. The conditions postulated are shown to correspond closely to the motion outside a free turbulent boundary, and good agreement is found between the predictions of the theory and the available experimental results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 1 , January 1955 , pp. 220 - 229
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

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