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On the scattering of water waves by a submerged slender barrier

Published online by Cambridge University Press:  17 February 2009

P. K. Kundu  and
N. K. Saha
P. K. Kundu
Affiliation:
Department of Applied Mathematics, Vidyasagar UniversityMidnapore-721102, INDIA
N. K. Saha
Affiliation:
Department of Mathematics, Bhatter College, P.O.: Dantan, Distt. Midnapore (W.B.), INDIA
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Abstract

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An approximate analysis, based on the standard perturbation technique, is described in this paper to find the corrections, up to first order to the reflection and transmission coefficients for the scattering of water waves by a submerged slender barrier, of finite length, in deep water. Analytical expressions for these corrections for a submerged nearly vertical plate as well as for a submerged vertically symmetric slender barrier of finite length are also deduced, as special cases, and identified with the known results. It is verified, analytically, that there is no first order correction to the transmitted wave at any frequency for a submerged nearly vertical plate. Computations for the reflection and transmission coefficients up to O(ε), where ε is a small dimensionless quantity, are also performed and presented in the form of both graphs and tables.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 2 , October 1998 , pp. 171 - 189
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]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. Appl. Math. 47 (1991) 23–32.CrossRefGoogle Scholar
[2]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.CrossRefGoogle Scholar
[3]Dean, W. R., “On the reflection of surface waves by a submerged plane barrier”, Proc. Camb. Phil. Soc. 41 (1945) 231–238.CrossRefGoogle Scholar
[4]Evans, D. V., “Diffraction of water waves by a submerged vertical plate”, J. Fluid Mech. 40 (1970) 433–451.CrossRefGoogle Scholar
[5]Evans, D. V., “A note on the waves produced by the small oscillations of a partially immersed vertical plate”, J. Inst. Maths Applic. 17 (1976) 135–140.CrossRefGoogle Scholar
[6]John, F., “Waves in the presence of an inclined barrier”, Comm. Pure Appl. Math. 1 (1948) 149–200.CrossRefGoogle Scholar
[7]Mandal, B. N. and Banerjea, S., “A note on waves due to rolling of a partially immersed nearly vertical plate”, SIAM J. Appl. Math. 51 (1991) 930–939.CrossRefGoogle Scholar
[8]Mandal, B. N. and Banerjea, S., “Solution of a boundary value problem associated with diffraction of water waves by a partially immersed nearly vertical barrier”, ZAMM 72 (1992) 517–519.CrossRefGoogle Scholar
[9]Mandal, B. N. and Chakrabarti, A., “A note on diffraction of water waves by a nearly vertical barrier”, IMA J. Appt.Math. 43 (1989) 157–165.CrossRefGoogle Scholar
[10]Mandal, B. N. and Goswami, S. K., “The scattering of an obliquely incident surface wave by a submerged fixed vertical plate”, J. Math. Phys. 25 (1984) 1780–1783.CrossRefGoogle Scholar
[11]Mandal, B. N. and Kundu, P. K., “Scattering of water waves by a submerged nearly vertical plate”, SIAM J. Appl. Math. 50 (1990) 1221–1231.CrossRefGoogle Scholar
[12]Shaw, D. C., “Perturbational results for diffraction of water waves by nearly vertical barriers”, IMA J. Appl. Math. 34 (1985) 99–117.CrossRefGoogle Scholar
[13]Ursell, F., “The effect of a fixed vertical barrier on surface waves in deep water”, Proc. Camb. Phil. Soc. 43 (1947) 374–382.CrossRefGoogle Scholar