Analytical Modelling And Frequency Band Characteristics Of The Resonant Reflection Of Ocean Surface Waves By Two Kinds Of Sinusoidal Sandbars

Firstly, ocean surface waves caused reflection by a finite array of sinu-soidal sandbars is analyzed, base on the technology of solving modified mild slope equation, we establish a Frobenius series of modified mild slope equation and give the expression of reflection coefficient and transmission coefficient.Moreover, in order to reveal the profound characters of water waves reflected by sandbars, we study water waves over an infinite array of singly periodic sinusoidal sandbars. Based on the Bloch theorem, we derive the formulation of band structure. From the calculation results, when the number of sand-bars reach sixteen, resonance band consistent with band gap, it mean that employ singly sinusoidal sandbars, however you change the numbers, height or width of sandbars, only can we find out a band gap which stop incident waves completely.Secondly, in order to find out a new type of sinusoidal sandbars which can form band gaps to stop multiple different frequency waves, we attempt to montage two sandbars with different period, forming composite sinusoidal sandbars and establishing a Frobenius series of modified mild slope equation,giving out the expression of reflection coefficient, transmission coefficient and formulation of band structure. We are delighted to find that several band gaps when the height of two periodic sandbars is different, composite sinusoidal sandbars can stop water waves absolutely in several fixed frequency interval, it mean that composite sinusoidal sandbars enlarge the ability of stopping incident waves.Bragg resonance occurs once the distance between two adjacent bars is the multiple of the half-wavelength of the normal incident waves, it is the mechanism of Bragg theorem, it mean that the sandbars topography only can occurs resonance with single fixed frequency incident waves, it is not the expect we want. Some scholars try to find out composite sandbars consist of double periods or three periods even more periods, from the results of they have found, composite sandbars can stop water waves absolutely in several fixed frequency interval. In this dissertation, we adopt another method,montage two sandbars with different periods, simple as it is, but it cans top water waves absolutely in two fixed frequency interval too; on the other hand, we exploit analytic solutions of modified mild slope equation, while few of scholars use it and most scholars use numerical solution or approximate analytical solution, analytic solution have advantages over than numerical solution or approximate analytical solution, so our solution can use to exploit mechanism of theoretical analysis.