Optimization Of Arched Bars And Cycloidal Bars For Maximum Bragg Resonant Reflection Of Linear Shallow Water Waves

To prevent the ocean waves from eroding the shoreline and protect the offshore constructions, in the past thirty years, Bragg breakwater, composed of a series of submerged artificial sand bars with the same size and shape, has been introduced and designed, and which always parallels to the coastline. The breakwater design is based on the Bragg resonance principle, which namely once the wavelength of ocean incident wave is twice the distance between the adjacent artificial sand bars, then Bragg resonance occurs and a water reflection wall will be formed to stop the ocean incident wave invade into the nearshore region. Therefore, many kinds of Bragg breakwater with different shapes of sand bar have been proposed, and widely studied. Nowadays, the optimal collocation of some Bragg breakwaters has been carried out, too. In this thesis, the optimal collocation of the Bragg breakwater with arched bars and cycloidal bars under the linear shallow water wave condition is conducted.In this thesis, firstly, under the two kinds of topography, including arched and cycloidal Bragg breakwaters, by applying the technique of the variable transform and matrix multiplication, for linear shallow water waves reflection by two kinds Bragg breakwater, the reflection coefficient analytical solution are obtained, and both in the Frobenius series form. These analytical series solutions are more accurate than Miles' theoretical solution obtained by using the perturbation method, once the relative height of the sand bar changes small them can agree well, but present analytical solutions still accurate when relative height of sand bar changes big, due to not restricted by the condition of the small parameter. Subsequently, we discuss the influence of the number of sand bars, relative width of sand bars and relative height of sand bars on the Bragg resonant reflection, the results show that once the distance between two adjacent sand bars is a half of the wavelength of the incident wave, there is a strong relation between these three quantities and the Bragg resonance reflection peak. In other words, these three quantities constitute a function with three variables on the Bragg resonant reflection coefficient. Based on this function relation, we obtain two groups of optimal collocation curves of the sand bar which constitutes the arched and cycloidal Bragg breakwaters,which may be very significant in the fundamental design of Bragg breakwaters. Finally,on the similarity among the results of these two kinds Bragg breakwaters of this thesis,and the parallel results in Liu et al. [25] parabolic Bragg breakwaters, we have carried on the preliminary discussion.