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Note on the interpretation of two-dimensional theories of growing cavities

Published online by Cambridge University Press:  28 March 2006

T. Brooke Benjamin
T. Brooke Benjamin
Affiliation:
Department of Engineering, University of Cambridge
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Abstract

It is shown in general how a two-dimensional flow can be justified as a physical approximation, notwithstanding the logarithmic singularity in pressure that occurs at infinity when the cavity expands or contracts at a varying rate. The argument presented, which affords a more natural interpretation than alternatives previously suggested, refers to the approximate equivalence-to a determinable degree of accuracy-between the hypothetical plane flow and the inner region of some real three-dimensional flow with small spanwise variations. The main ideas are illustrated by the example of a long ellipsoidal body which changes in volume while also undergoing shape perturbations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 1 , May 1964 , pp. 137 - 144
Copyright
© 1964 Cambridge University Press

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References

Birkhoff, G. 1950 Hydrodynamics. Princeton University Press.
Geurst, J. A. 1961 Linearized theory of two-dimensional cavity flows. Doctoral Dissertation, Technische Hogeschool, Delft.
Jeffreys, H. & Jeffreys, B. S. 1946 Methods of Mathematical Physics. Cambridge University Press.
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.
Wang, D. P. & Wu, T. Y. 1963 Small-time behaviour of unsteady cavity flows. Arch. Rat. Mech. Anal. 14, 127; also Calif. Inst. Tech. Hydrodynamics Lab. Rep. 97-3.Google Scholar
Woods, L. C. 1964 On the theory of growing cavities behind hydrofoils. J. Fluid Mech. 19, 124.Google Scholar
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