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

• Published in: Mathematics (Basel) 2021-08, Vol.9 (16), p.1876
• Main Authors: Zhai, Zhenfeng, Ye, Weifeng, Xia, Fei, Yang, Lele
• Format: Article
• Language: English
• Subjects: Addition theorem; analytical derivation; Cylinders; Eigenvectors; Exact solutions; Free surfaces; image principle; Incident waves; Investigations; Mathematical analysis; Mathematical models; Mathematics; Ocean engineering; Potential theory; Pressure distribution; Protective structures; Radiation; Velocity; Water depth; Water waves; Wave diffraction; wave elevation; wave force; Wave power
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math9161876

In this study, a semi-analytical model was developed to study wave diffraction around a concentric three-cylinder system near a wall based on linear potential theory. As a critical element, the target problem is transformed into bidirectional incident wave diffraction around two concentric structures based on the image principle and an analytical solution is obtained through eigenfunction expansion combined with a matching technique and Graf’s addition theorem. The validity of the proposed model was verified by comparing its results to known values. Parametric studies on porosity, annular spacing, incident angle, space between the structure and wall, and water depth were performed. The hydrodynamic loads and free-surface elevations in the system were calculated and compared to those reported in existing works on impermeable and permeable cylinders near a wall. The results indicate that the wave loads and run-ups on the exterior cylinder increase significantly based on the existence of the wall. However, based on the presence of an exterior porous protective structure, a significantly reduced influence of the wall on the interior cylinder can be observed. Considering the widespread use of concentric circular structures in ocean engineering, it is essential to conduct study on the hydrodynamic performance of concentric systems near walls, which can provide useful information for the design of marine structures.