Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-17T23:14:08.718Z Has data issue: false hasContentIssue false
  • English
  • Français

Complementary approximations to wave scattering by vertical barriers

Published online by Cambridge University Press:  26 April 2006

R. Porter  and
D. V. Evans
R. Porter
Affiliation:
School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK
D. V. Evans
Affiliation:
School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

Scattering of waves by vertical barriers in infinite-depth water has received much attention due to the ability to solve many of these problems exactly. However, the same problems in finite depth require the use of approximation methods. In this paper we present an accurate method of solving these problems based on a Galerkin approximation. We will show how highly accurate complementary bounds can be computed with relative ease for many scattering problems involving vertical barriers in finite depth and also for a sloshing problem involving a vertical barrier in a rectangular tank.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 294 , 10 July 1995 , pp. 155 - 180
Copyright
© 1995 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

Dean, W. R. 1945 On the reflexion of surface waves by a flat plate floating vertically. Proc. Camb. Phil. Soc. 41, 231–238.Google Scholar
Erdélyi A., Magnus, W., Oberhetting, F. & Tricomi, F. G. 1954 Tables of Integral Transforms. McGraw-Hill.
Evans, D. V. & Morris, C. A. N. 1972 Complementary approximations to the solution of a problem in water waves. J. Inst. Maths Applics. 10, 1–9.Google Scholar
Evans, D. V. 1970 Diffraction of surface waves by a submerged vertical plate. J. Fluid Mech. 40, 433–451.Google Scholar
Evans, D. V. & Mciver, P. 1987 Resonant frequencies in a container with a vertical baffle. J. Fluid Mech. 175, 295–307.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1981 Tables of Integrals, Series and Products. Academic Press.
Jarvis, R. J. 1971 The scattering of surface waves by two vertical plane barriers. J. Inst. Appl. Maths Applics. 7, 207–215.Google Scholar
John, F. 1948 Waves in the presence of an inclined barrier. Commun. Pure. Appl. Maths. 1, 149–200.Google Scholar
Jones, D. S. 1964 The Theory of Electromagnetism. Pergamon Press.
Levine, H. & Rodemich, E 1958 Scattering of surface waves on an ideal fluid. Math. and Stat. Lab. Tech. Rep. 78, Stanford University.
Lewin, M. 1963 The effect of vertical barriers on progressive waves. J. Math. Phys. 42, 287–300.Google Scholar
Mciver, P. 1985 Scattering of surface waves by two surface-piercing vertical barriers. IMA J. Appl Math. 35, 1–17.Google Scholar
Mei, C. C. 1966 Radiation and scattering of transient gravity waves by vertical plates. Q. J. Mech. Appl. Maths 19, 417–440.Google Scholar
Newman, J. N. 1974 Interaction of water waves with two closely spaced barriers. J. Fluid Mech. 66, 97–106.Google Scholar
Parsons, N. & Martin P. 1994 Scattering of water waves by submerged curved plates and by suface piercing plates Appl. Ocean Res. 16, 129–139Google Scholar
Porter, D. 1974 The radiation and scattering of surface waves by vertical barriers. J. Fluid Mech. 63, 625–634.Google Scholar
Smith, C. M. 1983 Some problems in linear water wave theory. PhD thesis, University of Bristol.
Ursell, F. 1947 The effect of a fixed vertical barrier on surface waves in deep water. Proc. Camb. Phil. Soc. 43, 374–382.Google Scholar
Wu, C. P. 1973 Variational and iterative methods for waveguides and arrays. In Computational Techniques for Electromagnetics (ed. R. Mittra), pp. 266–304. Pergamon