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Linearized planing-surface theory with surface tension. Part I: Smooth detachment

Published online by Cambridge University Press:  17 February 2009

E. O. Tuck
E. O. Tuck
Affiliation:
Department of Applied Mathematics, University of Adelaide, Box 498, G.P.O., Adelaide, South Australia 5001
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Abstract

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In the absence of surface tension, the problem of determining a travelling surface pressure distribution that displaces a portion of the free surface in a prescribed manner has been solved by several authors, and this “planing-surface” problem is reasonably well understood. The effect of inclusion of surface tension is to change, in a dramatic way, the singularity in the integral equation that describes the problem. It is now necessary in general to allow for isolated impulsive pressure, as well as a smooth distribution over the wetted length. Such pressure points generate jump discontinuities in free-surface slope. Numerical results are obtained here for a class of problems in which there is a single impulse located at the leading edge of the planing surface and detachment with continuous slope at the trailing edge. These results do not appear to approach the classical results in the limit as the surface tension approaches zero, a paradox that is resolved in Part II, which follows.

Type
Research Article
Information
The ANZIAM Journal , Volume 23 , Issue 3 , January 1982 , pp. 241 - 258
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions (Dover, New York, 1964).Google Scholar
[2]De Prima, C. R. and Wu, T. Y.-T., “On the theory of surface waves in water generated by moving disturbances,” California Institute of Technology, Engineering Division Report 21–23, 1957.Google Scholar
[3]Lamb, H., Hydrodynamics (Cambridge University Press, 1932).Google Scholar
[4]Muskhelishvili, N. I., Singular integral equations (Noordhoff, Croningen, 1953).Google Scholar
[5]Oertel, R. P., The steady motion of a flat ship including an investigation of local flow near the bow (Ph.D. Thesis, University of Adelaide, 1975).CrossRefGoogle Scholar
[6]Squire, H. B., “The motion of a simple wedge along the water surface”, Proc. Roy. Soc. A 243 (1957), 48–64.Google Scholar
[7]Wehausen, J. V. and Laitone, E. V., “Surface waves,” in Handb. der Physik, Vol. 9, ed. Flugge, S. (Springer-Verlag, Berlin, 1960).Google Scholar