Research On The Control Method Of Water Wave Based On The Principle Of Gradient Refractive Index Lens

Waves in nature have a certain amount of energy,which may cause adverse effects on the structures and seabed,riverbanks,coastal vegetation and aquatic life in waters.On the other hand,wave energy is also a kind of renewable source.Reasonable use of wave energy can somehow cope with the global energy demand and the limited situation of traditional fuels.Wave strength directly determines its destructiveness and availability,and so the control and guidance of wave propagation and the distribution of wave strength are of great significance.At present,the researches on surface waves in variable water depth mainly focus on the influences of gentle slopes and ocean ridges,and less attention has been paid to the guidance of surface waves by other underwater obstacles.Considering that the governing equation of surface water waves has a similar form with that of light waves,acoustic waves and electromagnetic waves,inspired by the wave control principle of variable refractive index lens,this paper attempts to apply the principles of optical Luneburg lens which can focus light and Eaton lens which make a rotation of light to the control and guidance of water surface waves.In this paper,the water depth is changed by an underwater obstacle with variable sections,so as to control the propagation path of surface waves,make the waves focus or rotation,and then change the distribution of the intensity of surface waves.Methods in this paper include theoretical derivation,numerical analysis and wave flume experiment.Firstly,the surface wave propagation equations are asymptotically expanded based on the ray method,and a form consistent with the optical equation is obtained under certain conditions.According to the refractive index distribution of Luneburg lens and Eaton lens,the morphologic functions of the underwater obstacles with variable sections corresponding to the two lens are calculated respectively.Then various obstacle models are designed according to different flow field conditions.Secondly,numerical simulations are conducted using COMSOL Multiphysics and experimental observations are carried out with a self-made wave flume system.The propagation paths and strength distribution of surface waves under the action of the designed variable-section obstacles are investigated to verify the theoretical analysis results.The results show that it is feasible to control and guide the propagation of surface water waves by underwater obstacles with variable sections based on the principle of variable refractive index lens.The numerical simulations and experimental observation results show that the underwater obstacles designed according to the Luneburg lens can focus the incident parallel waves on one point,which can significantly enhance the wave strength at that point.The underwater obstacles designed according to the Eaton lens can deflect the incident parallel waves,which makes the wave strength in the downstream area of the lens significantly reduced.