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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Panda, Srikumar Mondal, Arpita and Gayen, R 2016. An Efficient Integral Equation Approach to Study Wave Reflection by a Discontinuity in the Impedance-Type Surface Boundary Conditions. International Journal of Applied and Computational Mathematics,


    2015. Water Wave Scattering.


    Gayen, R. and Roy, Ranita 2013. An alternative method to study wave scattering by semi-infinite inertial surfaces. Journal of Marine Science and Application, Vol. 12, Issue. 1, p. 31.


    2011. Applied Singular Integral Equations.


    Squire, V.A. 2007. Of ocean waves and sea-ice revisited. Cold Regions Science and Technology, Vol. 49, Issue. 2, p. 110.


    (Chowdhury), Rupanwita Gayen Mandal, B. N. and Chakrabarti, A. 2005. Water-wave Scattering by an Ice-strip. Journal of Engineering Mathematics, Vol. 53, Issue. 1, p. 21.


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On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions

  • A. Chakrabarti (a1)
  • DOI: http://dx.doi.org/10.1017/S1446181100011925
  • Published online: 01 February 2009
Abstract
Abstract

Closed-form analytical expressions are derived for the reflection and transmission coefficients for the problem of scattering of surface water waves by a sharp discontinuity in the surface-boundary-conditions, for the case of deep water. The method involves the use of the Havelock-type expansion of the velocity potential along with an analysis to solve a Carleman-type singular integral equation over a semi-infinite range. This method of solution is an alternative to the Wiener-Hopf technique used previously.

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[1]D. V. Evans , “The solution of a class of boundary value problems with smoothly varying boundary conditions”, Q. J. Mech. Appl. Math. 38 (1994) 521536.

[3]C. Fox and V. A. Squire , “On the oblique reflection and transmission of ocean waves at shore fast sea ice”, Philos. Trans. Roy. Soc. London, Ser. A. 347 (1994) 185218.

[5]F. D. Gakhov , Boundary value problems (Pergamon, Oxford, 1966).

[6]I. M. Gradshteyn and I. S. Rhyzik , Tables of integrals, infinite series and products (Academic Press, 1980).

[7]J. B. Keller and M. Weitz , “Reflection and transmission coefficients of water waves entering or leaving an ice-field”, Comm. Pure Appl. Math. 6 (1953) 415417.

[11]A. S. Peters , “The effect of a floating mat on water waves”, Comm. Pure Appl. Math. 3 (1950) 319354.

[13]D. A. Spence ,“The lift coefficient of a thin jet flapped wing, II: A solution of the integro-differential equation for the slope of the jet”, Proc. R. Soc., Ser. A 261 (1961) 97118.

[16]E. Varley and J. D. A. Walker , “A method for solving singular integro-differential equations”, IMA J. of Appl. Math. 43 (1989) 1115.

[17]M. Weitz and J. B. Keller , “Reflection of water waves from floating ice in water of finite depth”, Comm. Pure Appl. Math. 3 (1950) 305318.

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The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
  • URL: /core/journals/anziam-journal
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