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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)
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]Evans D. V., “The solution of a class of boundary value problems with smoothly varying boundary conditions”, Q. J. Mech. Appl. Math. 38 (1994) 521536.
[2]Evans D. V. and Linton C. M., “On the step approximation for water wave problems”, J. Fluid Mech. 278 (1994) 229249.
[3]Fox C. and Squire V. A., “On the oblique reflection and transmission of ocean waves at shore fast sea ice”, Philos. Trans. Roy. Soc. London, Ser. A. 347 (1994) 185218.
[4]Gabov S. A., Sveshnikov A. G. and Shatov A. K., “Dispersion of internal waves by an obstacle floating on the boundary separating two liquids”, Prikl. Mat. Mech. 53 (1989) 727730, (Russian).
[5]Gakhov F. D., Boundary value problems (Pergamon, Oxford, 1966).
[6]Gradshteyn I. M. and Rhyzik I. S., Tables of integrals, infinite series and products (Academic Press, 1980).
[7]Keller J. B. and Weitz M., “Reflection and transmission coefficients of water waves entering or leaving an ice-field”, Comm. Pure Appl. Math. 6 (1953) 415417.
[8]Mitra R. and Lee S. W., Analytical techniques in the theory of guided wave (Mac-Millan, 1971).
[9]Muskhelishvili N. I., Singular integral equations (Gröningen, Holland, Nordhoff, 1953).
[10]Newman J. N., “Propagation of water waves over an infinite step”, J. Fluid Mech. 23 (1965) 399415.
[11]Peters A. S., “The effect of a floating mat on water waves”, Comm. Pure Appl. Math. 3 (1950) 319354.
[12]Sneddon I. N., The use of integral transforms (Tata McGraw Hill, New Delhi, 1974).
[13]Spence D. A.,“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.
[14]Stoker J. J., Water waves (Wiley Interscience, 1957).
[15]Ursell F., “The effect of a fixed vertical barrier on surface water waves in deep water”, Proc. Cambridge Philos. Soc. 43 (1947) 374382.
[16]Varley E. and Walker J. D. A., “A method for solving singular integro-differential equations”, IMA J. of Appl. Math. 43 (1989) 1115.
[17]Weitz M. and Keller J. B., “Reflection of water waves from floating ice in water of finite depth”, Comm. Pure Appl. Math. 3 (1950) 305318.
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  • ISSN: 1446-1811
  • EISSN: 1446-8735
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