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Water wave scattering by two submerged nearly vertical barriers

Published online by Cambridge University Press:  17 February 2009

B. N. Mandal  and
Soumen De
B. N. Mandal
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India; e-mail: biren@isical.ac.in.
Soumen De
Affiliation:
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700 108, India; e-mail: biren@isical.ac.in.
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Abstract

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The problem of surface water wave scattering by two thin nearly vertical barriers submerged in deep water from the same depth below the mean free surface and extending infinitely downwards is investigated here assuming linear theory, where configurations of the two barriers are described by the same shape function. By employing a simplified perturbational analysis together with appropriate applications of Green's integral theorem, first-order corrections to the reflection and transmission coefficients are obtained. As in the case of a single nearly vertical barrier, the first-order correction to the transmission coefficient is found to vanish identically, while the correction for the reflection coefficient is obtained in terms of a number of definite integrals involving the shape function describing the two barriers. The result for a single barrier is recovered when two barriers are merged into a single barrier.

Keywords

water wave scatteringlinear theoryperturbation analysisnearly vertical barriersreflection and transmission coefficients.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 1 , July 2006 , pp. 107 - 117
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Evans, D. V., “Diffraction of water waves by a submerged vertical plate”, J. Fluid Mech. 40 (1970) 433–451.CrossRefGoogle Scholar
[2]Evans, D. V., “A note on the wave produced by the small oscillations of a partially immersed vertical plate”, J. Inst. Maths. Applics. 17 (1976) 135–140.Google Scholar
[3]Evans, D. V. and Morris, C. A. N., “Complementary approximations to the solution of a problem in water waves”, J. Ints. Maths. Applics. 10 (1972) 1–9.CrossRefGoogle Scholar
[4]Jarvis, R. J., “The scattering of surface waves by two vertical plane barriers“, J. Inst. Maths. Applics. 7 (1971) 207–215.Google Scholar
[5]Kanoria, M. and Mandal, B. N., “Water wave scattering by a submerged circular arc shaped plate”, Fluid Dyn. Res. 31 (2002) 317–331.Google Scholar
[6]Levine, H. and Rodemich, F., “Scattering of surface waves on an ideal fluid”, Tech. Rep. No. 78, Stanford Univ., Math. Stat. La., 1958.Google Scholar
[7]Mandal, B. N. and Chakrabarti, A., “A note on diffraction of water waves by a nearly vertical barrier”, IMA J. Appl. Math. 43 (1989) 157–165.CrossRefGoogle Scholar
[8]Mandal, B. N. and Chakrabarti, A., Water Wave Scattering by Barriers (WIT Press, Southampton, 2000).Google Scholar
[9]Mandal, B. N. and Gayen (Chowdhury), R., “Water waves scattering by two symmetric circular arc shaped thin plates”, J. Engng. Math. 44 (2002) 297–303.Google Scholar
[10]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
[11]McIver, M. and Urka, U., “Wave scattering by circular arc shaped plates”, J. Engng. Maths. 29 (1995) 575–589.CrossRefGoogle Scholar
[12]McIver, P., “Scattering of water waves by two surface-piercing vertical barriers”, IMA J. Appl. Math. 35 (1985) 339–355.Google Scholar
[13]Midya, C., Kanoria, M. and Mandal, B. N., “Scattering of water waves by an inclined thin plate submerged in finite depth water”, Arch. Appl. Mech. 71 (2001) 827–840.CrossRefGoogle Scholar
[14]Parsons, N. F. and Martin, P. A., “Scattering of water waves by submerged plates using hypersingular integral equations”, Appl. Ocean Res. 14 (1992) 313–321.CrossRefGoogle Scholar
[15]Parsons, N. F. and Martin, P. A., “Scattering of water waves by submerged curved plates and by surface-piercing flat plates”, Appl. Ocean Res. 16 (1994) 129–139.CrossRefGoogle Scholar
[16]Porter, D., “The transmission of surface waves through a gap in a vertical barrier”, Proc. Camb. Phil. Soc. 71 (1972) 411–421.CrossRefGoogle Scholar
[17]Shaw, D. C., “Perturbational results for diffraction of water waves by nearly vertical barriers”, IMA J. Appl. Math. 34 (1985) 99–117.CrossRefGoogle Scholar
[18]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
[19]Williams, W. E., “Note on the scattering of water waves by a vertical barrier”, Proc. Camb. Phil. Soc. 62 (1966) 507–509.CrossRefGoogle Scholar