Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-28T19:14:53.170Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
Wu, T. Y. 1958 Unsteady supercavitating flows. Proc. 2nd Symp. on Naval Hydrodynamics, Washington, D.C., p. 293.