Analytical modeling of water wave interaction with a bottom-mounted surface-piercing porous cylinder in front of a vertical wall. (July 2019) - Cong, Peiwen
Abstract: The interaction of water wave with a bottom-mounted surface-piercing porous cylinder near a rigid vertical wall is investigated by an analytical model newly developed in the present work within the context of linear potential flow theory. The image principle is used to transfer the original problem in bounded water into the equivalent problem of wave interaction with two symmetrical porous cylinders in open seas in the presence of bi-directional incident waves. The velocity potential is analytically derived by means of the eigenfunction expansion along with the matching technique. Furthermore, a new alternative method for the evaluation of wave force is developed via the application of the Haskind–Hanaoka relation to a porous structure. In this method, an auxiliary radiation potential is introduced to replace the diffraction potential for the calculation of wave force. The auxiliary radiation potential used here is due to the oscillation of a porous cylinder in front of a wall. The image principle is used again to search the solution of the wave radiation problem in bounded water and the original radiation problem is then transferred to that due to two porous cylinders undergoing in-phase or out-of-phase motions in open seas. After the validation of the developed model, detailed parametric study is carried out. The porosity of the cylinder, incident wave heading and spacing between the cylinder and the wall are systematically adjusted to investigate their effects on the wave force as well as the wave elevation. The extension of our model to the case of a cylinder array in front of a wall has also been performed, and the associated phenomenon has been explored. Highlights: Image principle is used to transfer the original problem into the one in open seas. Relationship between Fourier coefficients of the real and image cylinders is given. No-flow condition at the original wall has been demonstrated. A new alternative method of wave force on the porous cylinder is developed. Extension of the model to an array of porous cylinders near a wall has been given.