Bragg reflection of linear shallow-water waves by an array of widely spaced trapezoidal bars on a fringing reef flat

A closed-form solution to the linear shallow-water wave equation for wave reflection by a finite periodic array of widely spaced trapezoidal bars on a fringing reef flat is presented. It is shown that, when the total number, height, or top width of the trapezoidal bars increases, the strength of the Bragg resonance increases but the downward shift of the resonance phase becomes more pronounced. When the width of the reef face increases or when the reef face changes from a concave profile to a convex profile, the strength of the Bragg resonance decreases and the downward shift of the resonance phase also becomes more pronounced. Especially, it is found that the location of trapezoidal bars plays an important role in the strength and occurrence condition of the Bragg resonant reflection. Finally, the optimal collocation of the location and width of trapezoidal bars is investigated. Considering both construction cost and reflecting capacity, the relative width is recommended to be within 0.4 <= wb/d <= 0.6 and the distance from the reef edge to trapezoidal bars is suggested to be equal to the spacing of trapezoidal bars.