Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-20T10:31:15.468Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffraction of oblique waves by an infinite cylinder

Published online by Cambridge University Press:  29 March 2006

Kwang June Bai
Kwang June Bai
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a numerical method for solving linearized water-wave problems with oscillatory time dependence. Specifically it considers the diffraction problem for oblique plane waves incident upon an infinitely long fixed cylinder on the free surface. The numerical method is based on a variational principle equivalent to the linearized boundary-value problem. Finite-element techniques are used to represent the velocity potential; and the variational principle is used to determine the unknown coefficients in the solution throughout the fluid domain. To illustrate this method, reflexion and transmission coefficients and the diffraction forces and moment are computed for oblique waves incident upon a vertical flat plate, a horizontal flat plate and rectangular cylinders, where the comparison is made with the existing results by others. Also considered is the associated sinuous forced-motion problem, where comparison is made with the results for a circular cylinder obtained by Bolton & Ursell (1973).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 3 , 15 April 1975 , pp. 513 - 535
Copyright
© 1975 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

Bai K. J. 1972 A variational method in potential flows with a free surface. Ph.D. dissertation, Department of Naval Architecture, University of California, Berkeley.
Black, J. L. & Mei C. C. 1970 Scattering and radiation of water waves. Water Resources and Hydrodynamics Laboratory, Department of Civil Engineering, Massachusetts Institute of Technology, Rep. no. 121.Google Scholar
Bolton, W. E. & Ursell F. 1973 The wave force on an infinitely long circular cylinder in an oblique sea. J. Fluid Mech. 57, 241–256.Google Scholar
Evans, D. V. & Morris C. A. N. 1972 The effect of a fixed vertical barrier on obliquely incident surface waves in deep water. J. Inst. Math. Appl. 9, 198–204.Google Scholar
Garrison C. J. 1969 On the interaction of an infinite shallow draft cylinder oscillating at the free surface with a train of oblique waves. J. Fluid Mech. 39, 227–255.Google Scholar
Lebreton, J. C. & Margnac M. A. 1966 Treatement sur ordinateur de quelques probltèmes concernant l'action de la houle sur les corps flottants en theorie bidimensionelle. Bulletin du Centre de Recherches et D'Essais de Chatou, no. 18, 3–43.Google Scholar
Mei, C. C. & Black J. L. 1969 Scattering of surface waves by rectangular obstacles in waters of finite depth. J. Fluid Mech. 38, 499–511.Google Scholar
Strang, G. & Fix G. 1973 An Analysis of the Finite Element Method. Prentice-Hal1.
Tong, P. & Pian T. H. H. 1973 On the convergence of the finite element method for problems with singularity. Int. J. Solid Structures, 9, 313–321.Google Scholar
Wehausen J. V. 1971 The motion of floating bodies. Ann. Rev. Fluid Mech. 3, 237–268.Google Scholar
Yamamoto, Y. & Tokuda N. 1973 Determination of stress intensity factors in cracked plates by the finite element method. Int. J. Numerical Method Engng, 6, 427–439.Google Scholar
Zienkiewicz O. Z. 1971 The Finite Element Method in Engineering Science. McGraw-Hill.