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First- and second-order forces on a cylinder submerged under a free surface

Published online by Cambridge University Press:  28 March 2006

T. Francis Ogilvie
T. Francis Ogilvie
Affiliation:
U.S. Office of Naval Research, London Branch Office
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Abstract

Several years ago Dean (1948) showed how to solve the linearized potential problem of water waves passing over a submerged circular cylinder. He discovered the remarkable fact that there is no reflexion from the cylinder; the transmitted waves have the same amplitude as the incident waves, but they suffer a phase shift in passing the cylinder. Soon after the publication of Dean's paper, Ursell (1950) investigated the problem anew. He placed the solution on a rigorous basis, supplied a uniqueness proof, and developed a form of the solution with which it was reasonable to perform calculations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 16 , Issue 3 , July 1963 , pp. 451 - 472
Copyright
© 1963 Cambridge University Press

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References

Dean, W. R. 1948 On the reflection of surface waves by a submerged cylinder. Proc. Camb. Phil. Soc., 44, 483–91.Google Scholar
Jahnke, E. & Emde, F. 1945 Tables of Functions. New York: Dover.
Milne-Thomson, L. M. 1960 Theoretical Hydrodynamics, 4th ed. New York: MacMillan.
Stoker, J. J. 1957 Water Waves. New York: Interscience.
Ursell, F. 1950 Surface waves on deep water in the presence of a submerged circular cylinder. I. Proc. Camb. Phil. Soc., 46, 141–52.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. Handbuch der Physik, Vol. IX. Berlin: Springer-Verlag.