Water wave interaction with a pair of floating and submerged coaxial cylinders in uniform water depth

摘要

Surge radiation problem due to two coaxial cylinders-one a riding hollow cylinder and the other a submerged solid cylinder of greater radius at some distance above an impermeable horizontal bottom-is solved analytically. Linear water wave theory and the method of separation of variables are used to obtain analytical expressions of the radiated velocity potential. In order to determine the unknown coefficients in the expressions, the eigenfunction expansion matching method is employed. Sets of hydrodynamic coefficients, namely, added mass and damping coefficient, for surge motion are obtained for different radii of the cylinders and for different gap between the cylinders. It is observed that change in radius, draft, and gap between the cylinders has significant effect on the hydrodynamic coefficients. The effect of the interior region of the hollow cylinder on the added mass and damping coefficient are presented. The hydrodynamic coefficients show very high oscillating behavior at a particular wavenumber which can be attributed to the occurrence of resonance in the interior region of the hollow cylinder. All the observations are presented through suitable graphs and compared with available results. Good agreement is observed with some established available results.