Band Structure Analysis Of Shallow-water Wave Over A Series Of Periodic Artificial Bar With Variable Depth

It is well known that in the crystal structure,the periodic arrangement of atoms and photons can produce modulation of electron waves and sound waves,resulting in energy band structure.Similarly,if the ocean waves over the seabed of the periodic structure of the terrain,also makes the ocean surface wave.If the band gap occurs in the band structure,then the frequency of water waves in the band gap will be banned,that is the formation of the total reflection.As early as the nineties,scientists have begun to pay attention to and study the Bloch waves.The Bloch wave related studies that have arisen over the cyclical oceanic terrain have yielded very important results.People on the coast can often find parallel to the coast and equidistant cyclical changes in the regular sand bars.These natural sand bars can reflect the waves of the sea,reducing the incidence of wave waves can erode the coast and destroy the coastal buildings.Natural sand bar is of great significance and value in ocean engineering and people began to focus on the establishment of artificial sand bars to protect the coast.In order to combine the stability of the artificial sand bar structure,this dissertation mainly studies the energy band of the semi-cosine shape,bow artificial bar and parabolic bar.In the first two decades,for the study of the water waves crossing the periodic terrain,which is the constant water depth,which includes the segmentation constant and the slice constant.But the semi-cosine-shaped bar,bow artificial bar and parabolic bar are variable water depth structure in this paper.The research content is shallow water wave crossing the series periodic analysis of energy band produced by artificial sand dam array.In the solution of the problem,the shallow water wave equation is used as the control equation.When solving the free surface elevation function in the deep water depth region,the Frobenius series expansion method is used to solve the series solution of the shallow water wave equation by using the variable substitution and Taylor series expansion and then use the Bloch principle to compute the band expression under the corresponding terrain.It can verify the accuracy of the band expression by comparing the region where the transmission coefficient tends to 0 and the region of the band energy.Finally,this paper discusses the influence of the parameters(such as width and so on)of the artificial sand bar array on the energy band structure,and gives the theoretical suggestions for the construction of artificial sand bars.In the practical offshore engineering,the construction and optimization of artificial sand bars provide valuable theoretical guidance.