A Note On The Radiation Problem of Water Waves In Presence of A Submerged Line Source With A Bottom Having Step Deformation
Uma Basu, Subhabrata Gangopadhyay
Keywords:- asymptotic representation, greenís identity, potential function, radiation problem, step deformation, submerged line source, wave amplitude.
Abstract:- Starting from an asymptotic representation of the velocity potential at infinite distances, the radiation problem of water waves due to a line source in presence of a bottom having step deformation is studied. Relations connecting amplitudes of radiated waves at infinite distances are worked out using Green's second identity. The general asymptotic forms of the potential form at infinite distances are written down in a discrete manner. A matrical representation connecting wave amplitudes is arrived at.
 A.G.Davies, The reflection of wave energy by undulations on the seabed, Dyn. Atoms. Oceans 7, pp. 207-232 (1982)
 A.G.Davies and A.D.Heathershaw, Surface wave propogation over sinusoidally varying topography, J.Fluid Mech., 144, pp. 419-443 (1984)
 C.C.Mei, Resonant reflection of surface water waves by periodic sand bars, J.Fluid Mech., 152, pp. 315-335 (1985)
 J.T.Kirby, A general wave equation for waves over rippled beds, J.Fluid Mech., 176, pp. 53-60 (1980)
 U. Basu and B.N.Mandal, Diffraction of water waves by a deformation of the bottom, Indian J.Pure and Appl. Math., 22(9), pp. 781-786 (1991)
 B.N.Mandal and U.Basu, Waves due to a line source in the presence of small bottom deformation, Int. J. Engg. Sci., Vol 31, No.1, pp. 71-75 (1993)
 J.W.Miles, Oblique surface-wave diffraction by a cylindrical obstacle, Dyn. Atoms. Oceans, 6, pp. 121-131 (1981)
 U. Basu and S. Mandal, Waves due to a line source in presence of undulatory bottom, Indian J. of Theo. Physics, Vol 51, No.2, pp. 105-113 (2002)
 R.C.Thorne, Multipole expression in the theory of surface waves, Proc. Camb. Phil. Soc., 49, pp. 707-716 (1953)
 P.F.Rhodes-Robinson, Fundamental Singularities in the theory of water waves with surface tensions, Bull. Austral. Math. Sec 2, pp. 317-333 (1970)
 D.V.Evans and C.M.Linton, On step approximations for water-wave problems, J.Fluid Mech., Vol 278, pp. 229-249 (1994)