Optimal collocation of Bragg breakwaters with rectangular bars on sloping seabed for Bragg resonant reflection by long waves

In this paper, we provide a closed-form analytical solution for the reflection of linear long waves propagating over a series of submerged rectangular breakwaters which are located on sloping seabed. It shows that the peak value of reflection coefficient decreases while the slope of seabed increases. And moreover, in view of the present analytical model, the magnitude of the peak Bragg resonant reflection should be affected by the number of breakwaters, dimensionless breakwater submergence and width for the given slope gradient of seabed. Finally, the optimal collocation curves for Bragg resonant reflection are presented for different number of breakwater. As applications, these optimal collocation curves can be used as quantitative indicators for engineers.