Evolution of Obliquely Interacting Wavetrains in Deep Water

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9972210The investigators conduct analytical, numerical, and experimental studies of three-dimensional water waves. They construct a state-of-the-art, precisely controlled, experimental facility that will enable the generation of nonlinear, three-dimensional wavefields and the direct measurement of their surface patterns. The goal is to use experiments to test and guide development of theoretical models and thereby obtain a unified experimental, theoretical, and numerical understanding of the evolution of nonlinear, three-dimensional surface waves over deep water. In particular they study (1) the dynamics of two obliquely interacting Stokes wavetrains, and (2) the dynamics of many obliquely interacting Stokes wavetrains that form resonantly interacting quartets.The investigators are building a precision facility in which to generate three-dimensional water waves with any desired shape, speed and complexity. One reason for these experiments is that an understanding of the fundamental physics of such waves greatly enhances the ability to model ocean waves. Models of ocean waves are necessary for a variety of applications, including shipping, construction, and defense. Models presently in use rest upon some mathematical assumptions that have never been tested and are possibly incorrect. The experiments of this project are designed to test these assumptions. A second reason for these experiments is that water waves are a physical application of the solutions to a special class of partial differential equations. These equations arise in many fields: oceanography, meteorology, plasma physics, and optics. Water waves provide a manageable experiment in which to study the application of the mathematics and to test the underlying assumptions and regimes of validity. If these equations model well the water wave experiments, then investigators in many fields have more confidence in applying them to other fields and in developing more such models. The project is supported by the Applied Mathematics and Computational Mathematics programs in the Division of Mathematical Sciences and by the Physical Oceanography program in the Division of Ocean Sciences.