## Diffraction and Radiation of Water Waves by Two Coaxial Vertical Cylinders

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2014

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The main objective of this thesis is to investigate the wave forces and hydrodynamic coefficients of two coaxial cylindrical structures in water of finite depth within the framework of linear water wave theory. We consider two coaxial vertical cylinders - one a riding hollow cylinder and the other a solid cylinder. This system consisting of two such vertical cylinders is considered as idealization of a buoy and a plate. In this study, we consider the fluid to be incompressible, homogeneous, inviscid, and the motion irrotational. First, the problem describing wave interaction with two coaxial cylindrical bodies, with one floating and the other submerged, is divided into two parts: one describing the diffraction of water waves by the fixed structure and the other describing the radiation of water waves by the body into otherwise calm water. It is to be noted that the radius of the submerged cylinder (lower solid cylinder) is greater than or equal to that of the floating cylinder (upper hollow cylinder). The radiation problem is further split into a number of parts, each of which corresponds to the moving body in a separate mode of motion. The physical problem involving diffraction or radiation is reduced to a boundary value problem governed by the threedimensional Laplace equation. The method of solution is based on the separation of variables and matched eigenfunction expansion technique. In the study of floating structures, an eigenfunction expansion, along with matching technique, is widely used due to its considerable accuracy. By using these techniques, the analytical expressions for the diffracted potentials and radiated potentials are presented, and by applying the appropriate matching conditions, which ensure the continuity of velocity and pressure along the virtual boundaries between two consecutive regions, we obtain a system of linear equations in each case which is solved for the unknown coefficients. The analytical expressions of the diffracted potentials and the radiated potentials, respectively, allow us to obtain the wave forces acting on the fixed cylindrical body and hydrodynamic coefficients, namely, the added mass and damping coefficient, acting on the cylindrical body for different modes of motion such as surge and roll. Since there exists no bottom for the hollow cylinder, we need to consider the translational wave force in the horizontal direction only. We carry out the investigation for two cases: first when the lower cylinder is bottom-mounted and then when it is raised to a finite height above the bottom. We also investigate our problem for the particular base case when the lower cylinder is absent, i.e., the case having only the floating cylinder tethered to the sea-bed.

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Supervisor: Swaroop Nandan Bora

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MATHEMATICS