A three-dimensional (3D) analytical solution for water wave scattering by comb-type caisson breakwaters is developed. Based on linear potential theory, the separation of variables coupled with periodic boundary condition are adopted to develop series solutions of velocity potentials. The convergence and correctness of newly developed analytical solution is confirmed. The formulae for hydrodynamic quantities calculating reflection and transmission coefficients and free surface elevations are given. Numerical examples are presented to investigate the effects of the structural and wave parameters on hydrodynamic quantities. The wave diffusive reflection are discussed. The variations in hydrodynamic quantities with the main influencing factors are clarified. The abrupt changes of the hydrodynamic quantities causing by the occurrence of multiple reflected and transmitted waves are estimated.


A comb-type caisson (CTC) breakwater (see Fig. 1) has been successfully built in Da-yao Bay of Dalian, China (Niu et al., 2003). The CTC consists of a rectangular caisson and two side plates. Compared with traditional gravity caisson breakwater, the CTC breakwaters can save engineering investment and reduce the requirement of foundation bearing capacity with a smaller base area, as the rectangular caisson is partially replaced by the side plates (Niu et al., 2001). According to engineering practice (Niu et al, 2003) and physical model tests (Li et al, 2002; Dong et al, 2003), 27% of the horizontal wave force was reduced and 24.5% of the construction investment was saved. More importantly, the gaps beneath the side plates allow the pass of fluid that can significantly reduce the flow velocity near the breakwater entrance which should be less than the 0.77 m/s for guaranteeing the navigation safety (Zhu et al., 2001).

The hydrodynamic performances of CTC breakwaters have been investigated by some scholars based on physical model tests and numerical simulations. Zhu et al. (2001) gave an overview on the construction of CTC breakwater in Da-yao bay of Dalian, and introduced the basic working mechanism of the CTC breakwater. Using the experimental data of wave forces acting on the side plates of CTC as the input wave load, Wang et al. (2001) conducted structural strength analysis and steel design for the side plates. Based on the finite element method, Zhang et al. (2002) further examined the internal stress distribution and the natural vibration characteristic for the side plates of CTC. Dong et al. (2003) carried out a series of physical model tests to measure the reflection coefficient and wave force on CTC breakwater, and they found that the reflection coefficient versus relative wave chamber width (the ratio of the wave chamber width to the incident wavelength) varies widely. By physical model tests, Fang et al. (2010) analyzed the distribution rule of wave pressure acting on CTC and confirmed that impulsive wave forces acting on CTC were probably caused due to the special configuration of CTC. And then Fang et al. (2011) developed a three-dimensional numerical wave tank to examine the hydrodynamic performances of CTC breakwaters using source wave-generation theory and gave an empirical formula that can simplify the calculation of the wave transmission coefficient. Recently, Zang et al. (2018) numerically and experimentally investigated the action mechanism of impulsive wave forces and then he gave some suggestions on improvements of hydrodynamic performance of CTC breakwaters.

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