Study Of Chaotic Phenomena Of Liquid Surface Wave Propagation In Periodic Structures And Wave

In the thesis, the propagation of liquid surface waves in periodic structures is studied experimentally and theoretically. This thesis consists of six chapters.In the first chapter, the backgrounds of liquid surface waves propagating in periodic structures are introduced, including the analogue to photonic crystals, recent progresses and our research motivations.In the second chapter, basic theories for liquid surface waves are briefly discussed. Several theoretical methods are developed to study the propagation of liquid surface waves in periodic structures, including transfer matrix method for 1D bottoms, multiple scattering method for 2D cylinder arrays, and plane wave method for periodically drilled bottom. Based on these methods, band structures, transmission and field distributions can be calculated.In the third chapter, the experimental methods of qualitative observation and quantitative measurement and the experimental setup are introduced. The design of source is also discussed.In the fourth chapter, we studied theoretically the omnidirectional total reflection for liquid surface waves propagating over a bottom with 1D periodic undulations. Band structure, transmission and reflection are calculated. Simulations based on a transfer matrix method including the traveling wave modes and evanescent wave modes demonstrate unambiguously the existence of omnidirectional total reflection. A general criterion for omnidirectional total reflection is found.In the fifth chapter, some new phenomena of liquid surface waves in the 2D systems are studied experimentally and theoretically, including focusing of a plane wave in the 2D cylinder arrays and negative refraction in the 2D periodically drilled bottom. Band structure and constant frequency contours analysis are carried out in order to understand these phenomena.In the sixth chapter, chaos in water waves is studied. With a double slit experiment, we find that the interference fringes disappear from the screen and the intensity obeys the addition rule after average if the source is placed in a billiard whose classical ray dynamics is chaotic. We thus demonstrate that dynamical chaos can induce phase randomization.