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A unified approach to problems of scattering of surface water waves by vertical barriers

  • A. Chakrabarti (a1), Sudeshna Banerjea (a2), B. N. Mandal (a3) and T. Sahoo (a1)

Abstract

A unified analysis involving the solution of multiple integral equations via a simple singular integral equation with a Cauchy type kernel is presented to handle problems of surface water wave scattering by vertical barriers. Some well known results are produced in a simple and systematic manner.

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Copyright

COPYRIGHT: © Australian Mathematical Society 1997

References

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[1] Banerjea, S., “Scattering of water waves by a vertical wall with gaps”, J. Austral. Math. Soc. Ser. B 37 (1996) 512–529.
[2] Chakrabarti, A. and Bharathi, L. Vijaya, “A new approach to the problem of scattering of water waves by vertical barriers”, ZAMM 72 (9) (1992) 415–423.
[3] Erdelyi, A., Magnus, W., Oberhittenger, F. and Tricomi, F. G., Tables of integral transforms. Volume 1 (McGraw Hill, New York, 1954).
[4] Evans, D. V., “Diffraction of water waves by a submerged vertical plate”, J. Fluid Mech. 40 (1970) 433–151.
[5] Evans, D. V., “Vertical barriers, sloping beaches and submerged bodies”, in Wave Asymptotics (eds. Martin, P. A. and Wickham, G. K.), (Cambridge University Press, 1992) 202–219.
[6] Gakhov, F. D., Boundary value problems (Addision Wesley, 1966).
[7] Gradshteyn, I. N. and Ryzhik, I. M., Tables of integrals, series and products (Acadamic press, 1980).
[8] Mandal, B. N. and Kundu, P. K., “Scattering of waterwaves by vertical barrier and associated mathematical methods”, Proc. Indian National Science Acadamy 53A (1987) 514–530.
[9] Mei, C. C., “Radiation and scattering of transient gravity waves by vertical plates”, Q. J. Mech. Appl. Math. 19 (1966) 417–440.
[10] Muskhelishvili, N. I., Singular integral equations (Noordhoff, 1963).
[11] Porter, D., “The transmission of surface waves through a gap in a vertical barrier”, Proc. Camb. Phil. Soc. 71 (1972) 411–421.
[12] Ursell, F., “The effect of a fixed vertical barrier on surface waves in deep water”, Proc. Camb. Phil. Soc. 43 (1947) 374–382.
[13] Bharathi, L. Vijaya and Chakrabarti, A., “Solution of a boundary value problem associated with diffraction of water waves by a nearly vertical barrier”, IMA J. App. Math. 47 (1991) 23–32.
[14] Bharathi, L. Vijaya, Chakrabarti, A., Mandal, B. N. and Banerjea, S., “Solution of the problem of scattering of water waves by a nearly vertical plate”, J. Austral. Math. Soc. Ser. B 35 (1994) 382–395.
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