Interface wave diffraction by bottom undulations in the presence of a thin plate submerged in lower fluid

• Autorzy: Dolai D. P. , Dolai P.
• Języki publikacji: EN

Abstrakty

EN

The problem of interface wave diffraction by bottom undulations in the presence of a thin vertical plate is investigated in this paper. The plate is submerged in the lower fluid of finite depth with bottom undulations and the upper fluid is of infinite height separated by a common interface. In the method of solution, we use a simplified perturbation analysis and suitable applications of Green's integral theorem in the two fluid regions produce first-order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom undulations and solution of the scattering problem involving a submerged vertical plate present in the lower fluid of uniform finite depth. For sinusoidal bottom undulations, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically by solving the zero-order reflection coefficient and suitable application of multi-term Galerkin approximations. The numerical results of zero-order and first-order reflection coefficients are depicted graphically against the wave number in a number of figures. An oscillatory nature of first-order reflection coefficient due to multiple interaction of the incident wave with bottom undulations is observed. The first-order reflection coefficient has a peak value for some particular value of the ratio of the incident wavelength and the bottom wavelength. The presence of the upper fluid has some significant effect on the reflection coefficients.

Słowa kluczowe

EN

interface wave diffraction; submerged vertical plate; perturbation analysis; sinusoidal bottom; Galerkin approximations; zero-order reflection coefficient; first-order reflection coefficient

PL

dyfrakcja fal; analiza zaburzeń; współczynnik odbicia

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2010
• Tom: Vol. 15, no 4
• Strony: 1017--1036
• Opis fizyczny: Bibliogr. 20 poz., wykr.

Twórcy

autor

Dolai D. P.

autor

Dolai P.

• River Research Institute, West Bengal 11A, Mirza Ghalib Street Kolkata-700 087, INDIA,

Bibliografia

• Davis A.G. (1982): The reflection of wave energy by undulations on the seabed. - Dyn. Atmos. Oceans, vol.6, pp.121-123.
• Davis A.G. and Heathershaw A.D. (1984): Surface wave propagation over sinusoidally varying topology. - J. Fluid Mech., vol.144, pp.419-443.
• Dean W.R. (1945): On the reflection of surface waves by a submerged plane barrier. - Proc. Camb. Phil. Soc., vol.41, pp.231-238.
• Evans D.V. (1970): Diffraction of water waves by a submerged vertical plate - J. Fluid Mech., vol.40, pp.433-451.
• 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.
• Hamilton J. (1977): Differential equations for long period gravity waves on fluid of rapidly varying depth. - J. Fluid Mech., vol.83, pp.289-310.
• Kreisel G. (1949): Surface waves. - Quart. Appl. Math., vol.7, pp.21-44.
• Lamb H. (1932): Hydrodynamics. - Cambridge University Press, pp.371.
• Losada I.J., Losada M.A. and Roldan A.J. (1992): Propagation of oblique incident waves past rigid vertical thin barriers. - Appl. Ocean Res., vol.14, pp.191-199.
• Maiti, Paramita and Mandal B.N. (2006): Scattering of oblique waves by bottom undulations in a two-layer fluid. - J. Appl. Math. and Computing, vol.22, pp.21-39.
• 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.
• 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.
• Mandal B.N. and Kundu P.K. (1987): Scattering of water waves by vertical barriers and associated mathematical methods. - Proc. Indian Natn. Sci. Acad., vol.53, pp.514-530.
• Miles J.W. (1967): Surface wave scattering matrix for a shelf. - J. Fluid Mech., vol.28, pp.755-767.
• Newman J.N. (1965): Propagation of water waves over an infinite step. - J. Fluid Mech., vol.23, pp.399-415.
• Porter D. (1972): The transmission of surface waves through a gap in a vertical barrier. - Proc. Camb. Phil. Soc., vol.71, pp.411-422.
• Porter R. and Evans D.V. (1995): Complementary approximations to waves scattering by vertical barriers. - J. Fluid Mech., vol.294, pp.160-186.
• Roseau M. (1976): Asymptotic wave theory. - North Holland, pp.311-347.
• Staziker D.J., Porter D. and Stirling D.S.G. (1996): The scattering of surface waves by local bed elevations. - Appl. Ocean Res., vol.18, pp.283-291.
• Ursell F. (1947): The effect of a fixed barrier on surface waves in deep water. - Proc. Camb. Phil. Soc., vol.43, pp.374-382.