Analytical modeling of water wave interaction with a bottom-mounted surface-piercing porous cylinder in front of a vertical wall

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 2 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.

Analytical Solution for Wave Diffraction by a Concentric Three-Cylinder System near a Vertical Wall

“…Additionally, the hydrodynamic loads on the outer and inner cylinders gradually decrease with an increasing β. An analogous phenomenon was observed by Teng and Ning [23] and Cong et al [30] for wave diffraction by impermeable and permeable cylinders near a wall. Additionally, based on the presence of the wall, the wave loads acting on the exterior structure are significantly larger than those in the unbounded water.…”

“…The validity of the proposed method was verified by comparing our results to the numerical results presented by Teng and Ning [23] and Cong et al [30]. When the porous parameter G 1 = 0, the concentric system becomes an impermeable cylinder, as discussed by Teng and Ning [23].…”

“…When b = c = 0 and the porous-effect parameter G 1 = 0, the structure becomes a porous cylinder, as discussed by Cong et al [30]. Figure 4 presents a comparison of the hydrodynamic loads on a porous cylinder near a wall derived by our method and by Cong et al [30] for b = c = 0, h/a = 5, G 1 = 1, and e/a = 1. One can see that the results are consistent, further validating the proposed method.…”

“…Konispoliatis et al [29] investigated the phenomenon of regular waves interacting with cylindrical arrays in front of infinite-length and finite-length vertical breakwaters. Cong et al [30,31] developed a novel analytical model to investigate the interactions between water waves and a permeable single cylinder near a wall, as well as a group of permeable cylinders near a wall. They evaluated both hydrodynamic loads and free-surface wave elevations.…”

Local Enhancements of the Mean Drift Wave Force on a Vertical Column Shielded by an Exterior Thin Porous Shell

“…Linear relations between the pressure drop across the porous geometry and the traversing velocity were derived by researchers, e.g., by using Darcy's law [1] or by using the convection neglected and porous effect modelled Euler equation [2]. The linear laws were adopted in many studies in assessing the functional performance of porous breakwaters of different types, such as vertical or submerged horizontal porous plates, perforated caissons, and porous columns [3][4][5][6][7][8]. Based on a linear resistance law, Zhao et al [9] examined the various hydrodynamic identities for porous structures.…”