Scattering of water waves by multiple segmented concentric semi-closed breakwaters and an interior cylinder: An analytical approach

• Published in: Physics of fluids (1994) 2023-12, Vol.35 (12)
• Main Authors: Miao, Jianming, Guo, Zhiqun, Zhai, Zhenfeng
• Format: Article
• Language: English
• Subjects: Boundary conditions; Breakwaters; Chebyshev approximation; Cylinders; Eigenvectors; Exact solutions; Incidence angle; Integral equations; Mathematical models; Model accuracy; Numerical analysis; Polynomials; Potential theory; Water waves
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0176194

This study aims to provide a theoretical analytical model for the design of breakwaters like Palm Jumeirah breakwater in Dubai by investigating the hydrodynamic characteristics of segmental semi-enclosed breakwaters simplified from it. An analytical solution to the interaction of water waves and a cylinder and multiple concentric segmented arc-shaped breakwaters has been developed based on linear potential theory. The eigenfunction matching method and separation of variables have been applied to expand the unknown function in terms of Chebyshev polynomials. By considering the boundary conditions, the integral equation has been simplified into a set of algebraic equations, which are then solved to determine the unknown function. The accuracy of the model has been confirmed by comparing the results with those in previous articles. The numerical analysis has revealed the relationship between variations in the hydrodynamic loads, wave elevation of the cylinder, and factors including the gap width between the arcs, opening angle, wave incidence angle, and porous-effect coefficient. The results indicate that segmented breakwaters offer better protection to the internal structure than unsegmented breakwaters. Moreover, segmented breakwaters with smaller gaps are less sensitive to diagonal waves and the gap can serve as a navigational channel, which is an extra benefit.