Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-08T16:31:01.521Z Has data issue: false hasContentIssue false
  • English
  • Français

Wave radiation and wave diffraction from a submerged body in a uniform current

Published online by Cambridge University Press:  20 April 2006

John Grue  and
Enok Palm
John Grue
Affiliation:
Department of Mechanics, University of Oslo, Blindern, Oslo 3, Norway
Enok Palm
Affiliation:
Department of Mechanics, University of Oslo, Blindern, Oslo 3, Norway
Get access Rights & Permissions [Opens in a new window]

Abstract

Radiation and diffraction of free-surface waves due to a submerged body in a uniform current is considered. The fluid layer is infinitely deep and the motion is two-dimensional. Applying the method of integral equations, the radiation problem and the diffraction problem for a submerged circular cylinder are examined. For small speed U of the current a forced motion of a given frequency will give rise to four waves. It is shown, however, that, for a circular cylinder, an incoming harmonic wave gives rise to two waves only. Depending on the frequency, the new generated wave may be considered as a transmitted or a reflected wave. The mean second-order force is computed. For the radiation problem the first-order damping force is also obtained. It is shown that, for some values of the parameters, the damping force is negative. This result is closely related to the fact that a harmonic wave travelling upstream with a phase velocity less than U conveys negative energy downstream. The forces remain finite as Uσ/g (σ ≡ the frequency, g ≡ the acceleration due to gravity) approaches ¼.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 151 , February 1985 , pp. 257 - 278
Copyright
© 1985 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

Abramowitz, M. & Stegun I. A.1972 Handbook of Mathematical Functions. Dover.
Acheson D. J.1976 On over-reflexion. J. Fluid Mech. 77, 433.Google Scholar
Cairns R. A.1979 The role of negative energy waves in some instabilities of parallel flows. J. Fluid Mech. 92, 1.Google Scholar
Dean W. R.1948 On the reflection of surface waves by a circular cylinder. Proc. Camb. Phil. Soc. 44, 483.Google Scholar
Evans D. V., Jeffrey D. C., Salter, S. H. & Taylor J. R. M.1979 Submerged cylinder wave energy device: theory and experiment. Appl. Ocean Res. 1, 3.Google Scholar
Grue, J. & Palm E.1984 Reflection of surface waves by submerged cylinders. Appl. Ocean Res. 6, no. 1.Google Scholar
Haskind M. D.1954 On wave motion of a heavy fluid. Prikl. Mat. Mekh. 18, 15.Google Scholar
Havelock T. H.1926 The method of images in some problems of surface waves Proc. R. Soc. Lond. A 115, 268.Google Scholar
Havelock T. H.1936 The forces on a circular cylinder submerged in a uniform stream Proc. R. Soc. Lond. A 157, 526.Google Scholar
Lamb H.1932 Hydrodynamics, 6th edn. Cambridge University Press.
Longuet-Higgins, M. S. & Stewart R. W.1960 Changes in the form of short gravity waves on long waves and tidal currents. J. Fluid Mech. 8, 565.Google Scholar
Newman J. N.1978 The theory of ship motions. Adv. Appl. Mech. 18, 221.Google Scholar
Ogilvie T. F.1963 First- and second-order forces on a cylinder submerged under a free surface. J. Fluid Mech. 16, 451.Google Scholar
Peregrine D. H.1976 Interaction of water waves and currents. Adv. Appl. Mech. 16, 9.Google Scholar
Tuck E. O.1965 The effect of non-linearity at the free surface on flow past a submerged cylinder. J. Fluid Mech. 22, 401.Google Scholar
Ursell F.1950 Surface waves on deep water in the presence of a submerged circular cylinder. I and II. Proc. Camb. Phil. Soc. 46, 141 and 153.Google Scholar
Ursell F.1973 On the exterior problems of acoustics. Proc. Camb. Phil. Soc. 74, 117.Google Scholar