Optimal Collocation Of Bragg Breakwaters For Bragg Resonance By Water Waves In The Whole Wave Range

The so-called Bragg breakwaters consist of a series of submerged artifcial barsparallel to the coastline. According to the Bragg’s law, once the Bragg’s condition ismet, i.e., the distance between two adjacent bars is about half of the wavelength of thenormally incident waves, then Bragg resonant refection occurs, which is quite signifcantin sheltering shores or localized structures from wave attack.Based on the explicit modifed mild-slope equation, this thesis studies the Braggresonant refection by three types of Bragg breakwaters with trapezoidal, rectifed cosi-noidal and parabolic bars.First, by using variable transform and Taylor series expansion and Frobenius seriesexpansion, analytical solutions to the explicit modifed mild-slope equation are obtainedfor wave refection by the three types of Bragg breakwaters. Second, by employing themultiplication rule of matrices, analytical expressions of refection coefcients are given.It is shown that the present solutions are more accurate than Miles’ theoretical formulawhich was derived by using the perturbation method with the relative height of thebars being the perturbation parameters. It is also shown that the agreement among thepresent solutions, experiment data and several numerical solutions is quite well, whichindicates the correctness of our solutions.The analytical solutions show that the magnitude of the peak Bragg resonant re-fection of the rectifed cosinoidal and parabolic bars depends solely on three bar param-eters, which are the bar number, the dimensionless bar height and the dimensionless barwidth. For the trapezoidal bar, the peak Bragg resonant refection still depends on theslopes of the front slope and back slope besides the aforementioned three parameters.Finally, based on intensive analysis of the relations among these parameters, three setsof optimal curves to determine the optimal collocation of the three types of breakwa-ters are established, which may be very signifcant in the fundamental design of Braggbreakwaters.