Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-20T08:11:35.399Z Has data issue: false hasContentIssue false
  • English
  • Français

On the short surface waves due to an oscillating, partially immersed body

Published online by Cambridge University Press:  29 March 2006

A. M. J. Davis
A. M. J. Davis
Affiliation:
Department of Mathematics, University College London
Get access Rights & Permissions [Opens in a new window]

Abstract

A body whose boundary C is vertical at the free surface F oscillates at high frequency in some prescribed manner. Asymptotic forms in terms of limit potentials are obtained for the upward force and the moment about a line in F of the pressure forces on the body. The cylindrical waves radiated to infinity are found to be asymptotically equivalent to those obtained in a two-dimensional solution of the Helmholtz equation. Some illustrative examples are given, principally the horizontal ellipsoid, in which case comparison with strip theory is possible.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 75 , Issue 4 , 25 June 1976 , pp. 791 - 807
Copyright
© 1976 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

Davis, A. M. J. 1971 Short surface waves due to an oscillating half immersed sphere Mathematika, 18, 20–39.Google Scholar
Davis, A. M. J. 1975a Small oscillations in a hemispherical lake Quart. J. Mech. Appl. Math. 28, 157–179.Google Scholar
Davis, A. M. J. 1975b Short surface waves due to a heaving sphere in a hemispherical lake J. Inst. Math. Appl. 16, 221–237.Google Scholar
Davis, A. M. J. 1975c Short surface waves due to a heaving torus Mathematika, 22, 122–134.Google Scholar
Hermans, A. J. 1973 A perturbation method for the radiation of short surface waves in three dimensions J. Engng Math. 7, 75–84.Google Scholar
Holford, R. L. 1964 Short surface waves in the presence of a finite dock I, II. Proc. Camb. Phil. Soc. 60, 957–810, 985–810.Google Scholar
Holford, R. L. 1965 On the generation of short two dimensional surface waves by oscillating surface cylinders of arbitrary cross section. Tech. Rep. Dept. Math., Stanford University, no. 4.Google Scholar
John, F. 1950 On the motion of floating bodies II Comm. Pure Appl. Math. 3, 45–101.Google Scholar
Keller, J. B., Lewis, R. M. & Seckler, B. D. 1956 Asymptotic solution of some diffraction problems Comm. Pure Appl. Math. 9, 207–265.Google Scholar
Leppington, F. G. 1970 On the radiation of short surface waves by a finite dock J. Inst. Math. Appl. 6, 319–340.Google Scholar
Leppington, F. G. 1972 On the radiation and scattering of short surface waves. Part 1 J. Fluid Mech. 56, 101–119.Google Scholar
Leppington, F. G. 1973a On the radiation and scattering of short surface waves. Parts 2 and 3. J. Fluid Mech. 59, 129–810, 147–810.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics, part II. McGraw-Hill.
Ogilvie, T. F. & Tuck, E. O. 1969 A rational strip theory of ship motions: I. Dept. Naval Archit. University of Michigan, Rep. no. 013.Google Scholar
Rhodes-Robinson, P. F. 1970a On the short wave asymptotic motion due to a cylinder heaving on water of finite depth I, II. Proc. Camb. Phil. Soc. 67, 423–810, 443–810.Google Scholar
Rhodes-Robinson, P. F. 1971 On the short cylindrical waves due to a body heaving on water Proc. Camb. Phil. Soc. 70, 311–321.Google Scholar
Rhodes-Robinson, P. F. 1972 On the short wave asymptotic motion due to a cylinder heaving on water of finite depth: III. Proc. Cambs. Phil. Soc. 72, 83–810.Google Scholar
Shen, M. C. 1975 Ray method for surface waves on fluid of variable depth SIAM Rev. 17, 38–56.Google Scholar
Ursell, F. 1953 Short surface waves due to an oscillating immersed body. Proc. Roy. Soc A 220, 90–103.Google Scholar
Ursell, F. 1954 Water waves generated by oscillating bodies Quart. J. Mech. Appl. Math. 7, 427–437.Google Scholar
Ursell, F. 1961 The transmission of surface waves under surface obstacles Proc. Camb. Phil. Soc. 57, 638–668.Google Scholar
Ursell, F. 1966 On the rigorous foundation of short-wave asymptotics Proc. Camb. Phil. Soc 62, 227–244.Google Scholar