Hydrodynamic of surge radiation by a floating cylinder in the presence of bottom-mounted cylindrical obstacle in a two-layer fluid system

In this study, the effects of the surge radiation force are investigated by a floating cylinder in two-layer fluid over a bottom-mounted cylinder. The proposed device consists of a floating cylinder in the upper layer and another a coaxial bottom cylinder in the lower layer of a two-layer fluid system of finite depth having the infinite horizontal extent. The radiation problem is taken into consideration under the framework of linear water wave and the entire fluid domain is divided into two regions, say, an exterior and interior regions. The analytical solutions for the surge radiation potential to the boundary-value problems in the respective regions are obtained by utilizing the method of separation of variables. By making use of the matched eigenfunction expansion method, the unknown coefficients that arise in the radiation potentials are evaluated. With the help of the expressions of the surge radiated potential, the corresponding radiation forces are obtained as a linear combination of added mass and damping coefficient. A bunch of numeric outcomes of added mass and damping coefficient are investigated for a distinct set of parameters of the device, i.e., the effect of the variation in frequencies with the radii of the cylinders, drafts of the floating cylinder, and the density ratio between the fluid layers on the surge radiated force are presented and their significant results are discussed. The 3D free surface and interface elevations due to the effect of surge radiated waves are presented in both surface- and internal-wave modes. The oscillations in added mass and damping coefficients are observed with variations of the parameters of the device.