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Scattering Of Water Waves In A Deep Ocean In Presence Of An Inertial Surface In Front Of A Thin Floating Dock

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 semi-infinite inertial surface on one half of the free surface and a thin floating semi-infinite 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 func tions 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. Hermans (11) applied integral equations to study free- surface waves interaction with a thick flexible dock. Mandal and De(12) investigated surface wave propagation over small undulation at the bottom of the ocean with surface discontinuity using an eigen function expansion method. The preset paper deals with the problem of scattering of water waves in presence of an semi-infinite inertial surface in front of a semi-infinite thin dock floating in deep water. The inertial surface is assumed to have uniform surface density. Appropriate Green's functions and velocity potential function in the regions occupied by water lead to integral expressions for the potential function in two different zones. Green's second identity is applied to the Green's functions and the potential function. The matching conditions along the vertical line of the surface of discontinuity suggest the continuity of pressure and velocity at the junction. Utilising the same, a pair of coupled Fredholm integral equation is arrived at, which can be solved by numerical methods. Since the water below the dock is undisturbed there will be no transmission of incoming wave train. An integral representation of the reflection coefficient is found out.