Scattering Of Water Waves In A Deep Ocean In Presence Of An Inertial Surface In Front Of A Thin Floating Dock
[Full Text]
AUTHOR(S)
Subhabrata Gangopadhyay, Uma Basu
KEYWORDS
Keywords:  Fredholm integral equation, Green’s function, Green’s second identity, inertial surface, reflection coefficient, semiinfinite dock, surface discontinuity.
ABSTRACT
Abstract:  The phenomenon of scattering of water waves is examined in presence of discontinuity at the free surface of a deep ocean. The surface discontinuity is thought of as originating due to the presence of a semiinfinite inertial surface on one half of the free surface and a thin floating semiinfinite dock on the other half. Appropriate expressions for Green's functions are set up for the fluid occupied in the inertial surface and for the fluid occupied below the thin dock. Employing Green's second integral theorem to the above mentioned Green's functions and the potential function the problem is reduced to finding out solutions of a pair of coupled Fredholm integral equation. An integral expression for the reflection coefficient is obtained.
REFERENCES
[1] K.O. Friedrich and H.Lewy, The dock problem, Comm.Applied Maths 1, pp. 135148 (1948)
[2] H.Chung, C.M.Linton, Reflection and transmission of waves across a gap between two semiinfinite elastic plates on water, J.Mech.Appl.Math 1 (1), pp. 115 (2004)
[3] D.V.Evans, T.V.Davies, Wateice interaction, Technical Report 1313, Stevens Institute of Technology (1968)
[4] R.V.Goldstein, A.V.Marchenko, The diffraction of plane gravitational waves by edge of an icecover, J.Appl. Math. Mech. (PMM), 53(6), pp. 731736 (1989)
[5] N.J.Balmforth, R.V.Craster, Ocean waves and ice sheets, J.Fluid Mech., 395, pp. 89124 (1999)
[6] H.Chung, C.Fox, Calculation of waveice interaction using the WienerHopf technique, NZ J.Math., 31, pp. 118 (2002)
[7] T.D.William, M.H.Meylan, The WienerHopf and residue calculus solutions for a submerged semiinfinite elastic plate, J.Eng. Math., 75, pp. 81106 (2012)
[8] A.S.Peters, The effect of a floating mat on water waves, Commun Pure Appl. Math., 3, pp. 319354 (1950)
[9] A.Chakraborti, On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions, ANZIAM J. 42, pp. 277286 (2000)
[10] A.Chakraborti, B.N.Mandal, R.Gayen, The dock problem revisited, Int.J.Math. Soc. 21, pp. 34593470 (2005)
[11] A.J.Hermans, Freesurface wave interaction with a thick flexible dock or very large floating platform, J.Eng.Math., 58, pp. 7790 (2007)
[12] B.N.Mandal, Soumen De, Surface wave propagation over small undulation at the bottom of an ocean with surface discontinuity, Geophysical and Astrophysical Fluid Dynamics, 103, pp. 1930 (2009)
[13] R.C.Thorne, Multiple expressions in the theory of surface waves, Math. Proc. Camb. Phil. Soc., 49, pp. 707715 (1953)
