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Solution of the problem of scattering of water waves by a nearly vertical plate

  • L. Vijaya Bharathi (a1), A. Chakrabarti (a1), B. N. Mandal (a2) and S. Banerjee (a3)

Abstract

An approximate solution is determined for the problem of scattering of water waves by a nearly vertical plate, by reducing it to two mixed boundary-value problems (BVP) for Laplace's equation, using perturbation techniques. While the solution of one of these BVP is well-known, the other BVPs is reduced to the problem of solving two uncoupled problems, and the complete solution of the problem under consideration up to first-order accuracy is derived with a special assumption on the shape of the plate and a related approximation. Known results involving the reflection and transmission coefficients are reproduced.

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References

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[1]Evans, D.V., “Diffraction of water waves by a submerged vertical plate”, J. Fluid Mech. 40 (1970) 433451.
[2]Mandal, B.N. and Chakrabarti, A., “A note on diffraction of water-waves by nearly vertical barriers”, IMA. J. Appl. Math. 43 (1989) 157165.
[3]Mandal, B.N. and Kundu, P.K., “Scattering of waterwaves by a submerged nearly vertical plate”, SIAM. J. Appl. Math. 50 (1990) 12211231.
[4]Mei, C.C., “Radiation and scattering of transient gravity waves by vertical plates”, Quart. Journ. Mech. Appl. Math. 19 (1966) 415440.
[5]Muskhelishvili, N.I., Singular integral equations, (Noordhoff, Groningen, 1953).
[6]Porter, D., “The transmission of surface waves through a gap in a vertical barrier”, Proc. Camb. Phil. Soc. 71 (1972) 411421.
[7]Shaw, D.C., “Perturbational results for diffraction of eater waves by nearly vertical barriers”, IMA. J. Appl. Math. 34 (1985) 99117.
[8]Stoker, , Water waves, (Wiley Inter Science, 1957).
[9]Ursell, F., “The effect of a fixed vertical barrier on surface waves in deep water”, Proc. Camb. Phil. Soc. 43 (1947) 374382.
[10]Bharathi, L. Vijaya and Chakrabarti, A., “Solution of a boundary value problem associated diffraction of water waves by a nearly vertical barrier”, IMA. J. Appl. Math. 47 (1991) 2332.
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