Manipulating The Liquid Surface Waves Based On The Band Properties And Transformation Medium

The research on the propagation phenomena and manipulating mechanisms of liquid surface waves not only contribute to expand and deepen the theoretical knowledge of wave propagation, but also have potential in engineering for disaster prevention, energy utilization and other applications. The thesis, based on band properties and transformation medium concept of liquid surface waves, conducts a study on manipulating mechanisms, methods and devices of liquid surface waves. The main contents are as follows:For the periodic array of rigid cylinders standing vertically in liquid, its band structure and constant frequency contour are calculated by using the multiple scattering theory. Considering the energy flow direction of the periodic structure, the propagation of liquid surface waves can be guided through the analysis of band structure and constant frequency contour. Thus, a certain arrangement of the cylinders is made to redirect the waves from a point source to four directions. Besides, the directional liquid surface wave emission is respectively obtained by the band edge states and resonant cavity states in the band structure. The feasibility of these theoretical methods is examined by the numerical calculation and experimental research.The transformation medium concept and gradient index (GRIN) ideas are invoked to the research of liquid surface wave manipulation. The principle and coordinate transformation method of liquid surface wave manipulation and realization of anisotropic liquid depths are illustrated. According to that gradually varied liquid depths can realize GRIN for liquid surface waves, the devices for wave bending, directional wave emission and wave focusing are developed and tested in the experiment. Corresponding experimental results show visually the waveguide phenomena of the devices at different frequencies. Comparative analyses of the results are also made.With the effective medium theory as the foundation, the analysis models and effective parameter equations in the long wavelength limit of the periodic array of rigid cylinders standing vertically in liquid and the system with periodic varied depth are derived. The influence factors for the effective parameters are analysed as well. The effective parameters are applied to design the GRIN devices for wave control. The devices of bend, Liineburg lens and directional emission for liquid surface waves are fabricated by employing the periodic arrays of rigid cylinders or periodically drilled bottoms with gradually varied parameters, and their waveguide properties are simulated in COMSOL. The waveguiding differences between the two designs, as well as their applicable conditions, are fully discussed.A GRIN lens for liquid surface waves is constructed through the gradual modification of the cylinder radii in an periodic cylinder array, and its wave focusing effect is verified in the experiment, which confirms the feasibility of designing wave control devices by using the effective parameters of periodic structures. The waveguide property of periodic slit array on the Fabry-Perot resonance condition is applied to design the waveguide devices of liquid surface waves. Based on this idea, new structure forms of shifter, bend and rotator for liquid surface waves are put forward. In addition, the concentrators for liquid surface waves are designed and fabricated, whose waveguide effects verified in the experiment prove the correctness and effectiveness of the calculation and analysis method.On the basis of theoretical analyses, numerical simulations and experimental studies, the thesis proposes the manipulation methods of liquid surface waves based on the band properties of periodic structures and transformation medium concept. Various kinds of wave control devices are designed and a lot of novel phenomena in wave propagations are observed and recorded in the experiments, the research results of which can be applied to manipulate the propagations of water waves and solve the practical problems in ocean science or hydraulic engineering.