Optimal Collocation of Three Kinds of Bragg Breakwaters for Bragg Resonant Reflection by Long Waves

Abstract

It is well known that, for a series of submerged artificial bars uniformly distributed in the coastal region parallel to the coastline, if the wavelength of the incident wave train is twice that of the bar distance, Bragg resonant reflection occurs. In this paper, three closed-form analytical solutions for linear long-wave reflection for bars with triangular shape, rectified cosinoidal shape, and idealized trapezoidal shape are presented. These analytical solutions show that the magnitude of the peak Bragg resonant reflection still depends on three bar parameters, which are the bar number, the dimensionless bar height, and the dimensionless bar width. Based on intensive analysis of the relations among these parameters, three sets of optimal curves to determine the optimal collocation of the three types of artificial bars are established, which may be very significant in the study of Bragg resonance and in the fundamental design of Bragg breakwaters.