Hydrodynamics of a body floating in a two-layer fluid of finite depth. Part 2. Diffraction problem and wave-induced motions

Abstract

A linearized two-dimensional diffraction problem in a two-layer fluid of finite depth was solved for a general floating body and relevant wave-induced motions were studied. In a two-layer fluid, for a prescribed frequency, incident waves propagate with two different wave modes. Thus the wave-exciting forces and resulting motions must be computed separately for each mode of the incident wave. The boundary integral equation method developed by the authors in the Part-1 article was applied to directly obtain the diffraction potential (pressure) on the body surface. With the computed results, an investigation was carried out on the effects of the fluid density ratio and the interface position on the wave-exciting forces on the body and the motions of the body, including the case in which the body intersects the interface. By a systematic derivation using Green's theorem, all the possible reciprocity relations were derived theoretically in explicit forms for a system of finite depth; these relations were confirmed to be satisfied numerically with very good accuracy. Experiments were also carried out using water and isoparaffin oil as the two fluids and a Lewis-form body. Measured results for the sway- and heave-exciting forces and the heave motion were compared with the computed results, and a favorable agreement was found.