Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T13:27:59.327Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffraction of water waves by a submerged vertical plate

Published online by Cambridge University Press:  29 March 2006

D. V. Evans
D. V. Evans
Affiliation:
Department of Mathematics, University of Bristol
Get access Rights & Permissions [Opens in a new window]

Abstract

A thin vertical plate makes small, simple harmonic rolling oscillations beneath the surface of an incompressible, irrotational liquid. The plate is assumed to be so wide that the resulting equations may be regarded as two-dimensional. In addition, a train of plane waves of frequency equal to the frequency of oscillation of the plate, is normally incident on the plate. The resulting linearized boundary-value problem is solved in closed form for the velocity potential everywhere in the fluid and on the plate. Expressions are derived for the first- and second-order forces and moments on the plate, and for the wave amplitudes at a large distance either side of the plate. Numerical results are obtained for the case of the plate held fixed in an incident wave-train. It is shown how these results, in the special case when the plate intersects the free surface, agree, with one exception, with results obtained by Ursell (1947) and Haskind (1959) for this problem.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 40 , Issue 3 , 18 February 1970 , pp. 433 - 451
Copyright
© 1970 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, 231–8.Google Scholar
Haskind, M. D. 1948 The pressure of waves on a barrier. Inzhenernyi Sbornik, 4, 147–60.Google Scholar
Haskind, M. D. 1959 Radiation and diffraction of surface waves by a flat plate floating vertically. Prikl. Mat. Mekh. 23, 546. (English translation 1959 Appl. Math. Mech. 23, 770–83.)Google Scholar
John, F. 1948 Waves in the presence of an inclined barrier. Comm. Pure Appl. Math. 1, 149–200.Google Scholar
Keulegan, G. H. & Carpenter, L. H. 1958 Forces on cylinders and plates in an oscillating fluid. J. Res. Natn. Bur. Stan. 60, 423–40.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lewin, M. 1963 The effect of vertical barriers on progressing waves. J. Math. Phys. 42, 287–300.Google Scholar
Mei, C. C. 1966 Radiation and scattering of transient gravity waves by vertical plates. Quart. J. Mech. Appl. Math. 19, 417–40.Google Scholar
Muskhelishvili, N. I. 1963 Singular Integral Equations. (Translation by J. R. M. Radok.) Groningen, Holland:Noordhoff.
Ogilvie, T. F. 1963 First- and second-order forces on a cylinder submerged under a free surface. J. Fluid. Mech. 16, 451–72.Google Scholar
Robinson, A. & Laurmann, J. A. 1956 Wing Theory. Cambridge University Press.
Sedov, L. I. 1965 Two-dimensional Problems in Hydrodynamics and Aerodynamics. New York: Interscience.
Tuck, E. O. 1970 Transmission of water waves through small apertures. J. Fluid Mech. (submitted.)Google Scholar
Ursell, F. 1947 The effect of a fixed vertical barrier on surface waves in deep water. Proc. Camb. Phil. Soc. 43, 374–82.Google Scholar
Ursell, F. 1948 On the waves due to the rolling of a ship. Quart. J. Mech. Appl. Math. 1, 246–52.Google Scholar
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
Watson, G. N. 1940 Theory of Bessel Functions. Cambridge University Press.
Wehausen, J. V. & Laitone, E. V. 1960 Surface Waves. Handb. Phys. vol. IX, 446–778. Berlin: Springer.