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Oblique diffraction of surface waves by a submerged vertical plate

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Abstract

A train of small-amplitude surface waves is obliquely incident on a fixed, thin, vertical plate submerged in deep water. The plate is infinitely long in the horizontal direction. An appropriate one-term Galerkin approximation is employed to calculate very accurate upper and lower bounds for the reflection and transmission coefficients for any angle of incidence and any wave number thereby producing very accurate numerical results.

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References

  1. W. R. Dean, On the reflection of surface waves by a submerged plane barrier. Proc. Camb. Phil. Soc. 41 (1945) 231–238.

    Google Scholar 

  2. 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 

  3. T.H. Havelock, Forced surface waves on water. Phil. Mag. 8 (1929) 569–576.

    Google Scholar 

  4. H. Levine and E. Rodemich, Scattering of surface waves on an ideal fluid. Stanford Univ. Tech. Rep. No. 78, Math. and Stat. Lab. Stanford (1958) pp 1–64.

  5. W.E. Williams, Note on the scattering of water waves by a vertical barrier. Proc. Camb. Phil. Soc 62 (1966) 507–509.

    Google Scholar 

  6. S.K. Goswami, A note on the problem of scattering of surface waves by a submerged fixed vertical barrier. ZAMM 62 (1982) 637–639.

    Google Scholar 

  7. B.N. Mandal and P.K. Kundu, Scattering of water waves by vertical barriers and associated mathematical methods. Proc. Indian Natn. Sci. Acad. 53 (1987) 514–530.

    Google Scholar 

  8. B.N. Mandal and P.K. Kundu, A note on the reflection coefficients in a water wave scattering problem. Appl. Math. Lett. 3 (1990) 5–7.

    Google Scholar 

  9. D.V. Evans, Diffraction of water waves by a submerged vertical plate. J. Fluid Mech. 40 (1970) 433–451.

    Google Scholar 

  10. T.R. Faulkner, The diffraction of an obliquely incident surface wave by a submerged plane barrier. ZAMP 17 (1965) 699–707.

    Google Scholar 

  11. T.R. Faulkner, The diffraction of an obliquely incident surface wave by a vertical barrier of finite depth. Proc. Camb. Phil. Soc. 62 (1966) 829–838.

    Google Scholar 

  12. R.J. Jarvis and B.S. Taylor, The scattering of surface waves by a vertical barrier. Proc. Camb. Phil. Soc. 66 (1969) 417–422.

    Google Scholar 

  13. D.V. Evans and C.A.N. Morris, The effect of a fixed vertical barrier on oblique incident surface waves in deep water. J. Inst. Maths. Aplics. 9 (1972) 198–204.

    Google Scholar 

  14. B.N. Mandal and S.K. Goswami, A note on the diffraction of an obliquely incident surface waves by a partially immersed fixed vertical barrier. Appl. Sci. Res. 40 (1983) 345–353.

    Google Scholar 

  15. B.N. Mandal and S.K. Goswami, A note on the scattering of surface waves obliquely incident on a submerged fixed vertical barrier. J. Phys. Soc. Jpn. 53 (1984) 2980–2987.

    Google Scholar 

  16. B.N. Mandal and S.K. Goswami, The scattering of an obliquely incident surface waves by a submerged fixed vertical plate. J. Math. Phys. 25 (1984) 1780–1783.

    Google Scholar 

  17. B.N. Mandal and D.P. Dolai, Oblique water wave diffraction by thin vertical barriers in water of uniform finite depth. Appl. Ocean Res. 16 (1994) 195–203.

    Google Scholar 

  18. B.N. Mandal and P.K. Kundu, A note on scattering of water waves by a submerged nearly vertical plate. SIAM J. Appl. Math. 50 (1990) 1221–1231.

    Google Scholar 

  19. Sudeshna Banerjea and B.N. Mandal, Solution of a singular integral equation in a double interval arising in the theory of water waves. Appl. Math. Lett. 6 (1993) 81–84.

    Google Scholar 

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Mandal, B.N., Das, P. Oblique diffraction of surface waves by a submerged vertical plate. J Eng Math 30, 459–470 (1996). https://doi.org/10.1007/BF00049246

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  • DOI: https://doi.org/10.1007/BF00049246

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