Internal Wave Diffraction by a Strip of an Elastic Plate on the Surface of a Stratified Fluid
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Department of Mathematics Prasanna Deb Women’s College Jalpaiguri-735101 West Bengal, INDIA
River Research Institute Govt. of West Bengal 11A, Mirza Ghalib Stret Kolkata-700087, INDIA
Online publication date: 2013-04-19
Publication date: 2013-03-01
International Journal of Applied Mechanics and Engineering 2013;18(1):5-26
The problem of internal wave diffraction by a strip of an elastic plate of finite width present on the surface of an exponentially stratified liquid is investigated in this paper. Assuming linear theory, the problem is formulated in terms of a function related to the stream function describing the motion in the liquid. The related boundary value problem involves a hyperbolic type partial differential equation (PDE), known as the Klein Gordon equation. The method of Wiener-Hopf is utilized in the mathematical analysis to a slightly generalized boundary value problem (BVP) by introducing a small parameter, and the problem is solved approximately for large width of the plate. In the final results, this small parameter is made to tend to zero. The diffracted field is obtained in terms of integrals, which are then evaluated asymptotically in different regions for a large distance from the edges of the plate and the results are interpreted physically.
Dolai P. and Mandal B.N. (2007): Scattering of internal waves in a stratified fluid by the edge of an inertial surface. - Bull. Cal. Math. Soc., vol.99, pp.5-20.
Gabov S.A. and Svesnikov A.G. (1982): On the diffraction of internal waves by the edge of an ice field. - Soviet. Math. Dokl., vol.26, pp.8-11.
Gayen R., Mandal B.N. and Chakrabarti A. (2007): Water wave diffraction by a surface strip. - J. Fluid Mech., vol.571, pp.419-438.
Gayen R., Mandal B.N. and Chakrabarti A. (2006): Water wave scattering by two sharp discontinuities in the surface boundary conditions. - IMA J. Appl. Math., vol.71, pp.811-831.
Kanoria M., Mandal B.N. and Chakrabarti A. (1999): The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena. - Wave Motion, vol.29, pp.267-292.
Noble B. (1958): Methods based on the Wiener-Hopf technique for the solution of partial differential equations. - New York: Pergamon Press.
Varlamov V.V. (1983): Diffraction of internal waves in a stratified liquid on a semi-infinite wall. - U.S.S.R. Comput. Maths. Math. Phys., vol.23, pp.87-91.
Varlamov V.V. (1985): The scattering of internal waves by the periphery of an elastic plate. - U.S.S.R. Comput. Maths. Math. Phys., vol.25, pp.58-63.
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