Oblique water wave diffraction by a step

• Autorzy: Dolai P.

Identyfikatory

DOI

10.1515/ijame-2017-0003

• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with the problem of diffraction of an obliquely incident surface water wave train on an obstacle in the form of a finite step. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials are utilized to obtain a very accurate numerical estimate for reflection and transmission coefficients which are depicted graphically. From these figures various interesting results are discussed.

Słowa kluczowe

EN

finite step; Havelock expansion; Galerkin approximation; Gegenbauer polynomial; reflection and transmission coefficients

PL

aproksymacja Galerkina; wielomian Gegenbauera; odbicie

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2017
• Tom: Vol. 22, no. 1
• Strony: 35--47
• Opis fizyczny: Bibliogr. 19 poz., rys., tab., wykr.

Twórcy

autor

Dolai P.

• Department of Mathematics Prasannadeb Women's College Jalpaiguri-735101, West Bengal, INDIA

Bibliografia

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• [2] Ursell F. (1947): The effect of a fixed barrier on surface waves in deep water. Proc. Camb. Phil. Soc., vol.43, pp.374-382.
• [3] Evans D.V. (1970): Diffraction of water waves by a submerged vertical plate. J. Fluid Mech., vol.40, pp.433-451.
• [4] Porter D. (1972): The transmission of surface waves through a gap in a vertical barrier. Proc. Camb. Phil. Soc., vol.71, pp.411-422.
• [5] Mandal B.N. and Dolai D.P. (1994): Oblique water wave diffraction by thin vertical barriers in water of uniform finite depth. Appl. Ocean Res., vol.16, pp.195-203.
• [6] Roseau M. (1976): Asymptotic wave theory. North Holland, pp.311-347.
• [7] Kreisel G. (1949): Surface waves. Quart. Appl. Math., vol.7, pp.21-44.
• [8] Fitz-Gerald G.F. (1976): The reflection of plane gravity waves traveling in water of variable depth. Phil. Trans. Roy. Soc. Lond., vol.34, pp.49-89.
• [9] Hamilton J. (1977): Differential equations for long period gravity waves on fluid of rapidly varying depth. J. Fluid Mech., vol.83, pp.289-310.
• [10] Newman J.N. (1965): Propagation of water waves over an infinite step. J. Fluid Mech., vol.23, pp.399-415.
• [11] Miles J.W. (1967): Surface wave scattering matrix for a shelf. J. Fluid Mech., vol.28, pp.755-767.
• [12] Mandal B.N. and Gayen, Rupanwita (2006): Water wave scattering by bottom undulations in the presence of a thin partially immersed barrier. Appl. Ocean Res., vol.28, pp.113-119.
• [13] Dolai D.P. and Dolai P. (2010): Interface wave diffraction by bottom undulations in the presence of a thin plate submerged in lower fluid. Int. J. Appl. Mech. and Engg. vol.15, pp.1017-1036.
• [14] Stoker J.J. (1957): Water Waves. New York: Interscience.
• [15] Wehausen J.V. and Laiton E.V. (1960): Surface Waves. Handbuch der Physik: Springer.
• [16] Bartholomeusz E.F. (1958): The reflection of long waves at a step. Proc. Camb. Phil. Soc., vol.54, pp.106-118.
• [17] Evans D.V. and McIver P. (1984): Edge waves over a shelf: full linear theory. J. Fluid Mech., vol.142, pp.79-95.
• [18] Havelock T.H. (1929): Forced surface waves on water. Phil. Mag., vol.8, pp.569-576.
• [19] Kanoria M., Dolai D.P. and Mandal B.N. (1999): Water wave scattering by thick vertical barriers. J. Eng. Math., vol.35, pp.361-384.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)