# Scattering of surface water waves involving a vertical barrier with a gap

- 96 Downloads
- 9 Citations

## Abstract

A mixed boundary-value problem associated with scattering of surface water waves by a vertical barrier with a gap of an arbitrary length is solved completely by the aid of the solution of a special logarithmic singular integral equation in the domain (*a*,*b*), which has bounded behaviour at both the end points *a*(>0) and *b*. The reflection coefficient is obtained analytically and its numerical values are presented graphically, for different values of the ratio of the width of the gap to the position of the gap. The present method of solution replaces the existing methods, which are either more elaborate or approximate in nature.

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.F. Ursell, The effect of a fixed vertical barrier on surface waves in deep water.
*Proc. Camb. Phil. Soc.*43 (1947) 374–382.Google Scholar - 2.W.E. Williams, A note on scattering of water waves by a vertical barriers.
*Proc. Camb. Phil. Soc.*62 (1966) 507–509.Google Scholar - 3.A. Chakrabarti, A survey on two mathematical methods used in scattering of surface water waves. In: B.N. Mandal (ed.),
*Advances in Fluid Mechanics, Mathematical Techniques for water waves*. Southampton Boston: Computational Mechanics Publications (1997) pp. 231–249.Google Scholar - 4.S. Banerjea and C.C. Kar, A note on some dual integral equations.
*ZAMM*80 (2000) 205–210.Google Scholar - 5.E.O. Tuck, Transmission of water waves through small apertures.
*J. Fluid Mech.*49 (1971) 65–74.Google Scholar - 6.D. Porter, The transmission of surface waves through a gap in a vertical barrier.
*Proc. Camb. Phil. Soc.*71 (1972) 411–421.Google Scholar - 7.C.C. Mei, Radiation and scattering of transient gravity waves by vertical plates.
*Quart. J. Mech. Appl. Math.*19 (1966) 417–440.Google Scholar - 8.J.J. Stoker, Surface waves in water of variable depth.
*Quart. Appl. Math.*5 (1947) 1–54.Google Scholar - 9.B.N. Mandal and A. Chakrabarti,
*Water Wave Scattering by Barriers*. Southapmton: WIT press (2000) 390 pp.Google Scholar - 10.I.S. Gradshteyn and I.M. Ryzhik,
*Table of Integrals, Series and Products*. London: Academic press (1980) 1160 pp.Google Scholar - 11.A. Chakrabarti and S.R. Manam, Solution of the logarithmic singular integral equation, to appear in Appl. Math. Letters.Google Scholar
- 12.R. Estrada and R.P. Kanwal, Integral equations with logarithmic kernels.
*IMA Jour. of Appl. Math.*43 (1989) 133–155.Google Scholar - 13.F.D. Gakhov,
*Boundary Value Problems*. New York: Pergmon Press (1966) 561 pp.Google Scholar