9407030 Hou This project will support research on several problems in the areas of fluid mechanics and materials science. Specifically, three-dimensional subharmonic instability of three-dimensional Stokes waves, three-dimensional weak water-wave turbulence, singularity formation in fluid interfaces strongly mediated by surface tension, reconnection of fluid interfaces, and interaction of ocean free surfaces with moving objects will be studied. Investigations will be conducted on fundamentally difficult fluid dynamical and materials problems by developing and applying robust, efficient computational tools, including novel time integration schemes allowing large time-steps, spectrally accurate spatial discretizations, fast summation techniques and the level set formulation which can effectively compute flows undergoing topological changes. Large-scale computation and computational mathematics are now primary tools in studying physical processes characterized by randomness and strong nonlinearity. Such processes include complex pattern formation and growth problems in diffusion dominated systems, and wave interactions on the ocean's free surface. Closely related are problems with singular or near singular behavior, such as flows undergoing changes in topological type, or the breaking of water waves. These fluid dynamical and materials problems will be studied by developing and applying state-of-the-art numerical methods to large-scale computation, and through analytical, numerical and modeling studies of important constituent processes. The research will promote inter-disciplinary interactions among applied mathematicians, physicists and material scientists and should have a potential impact in application areas such as high performance computation, interfacial fluid dynamics, and materials science. The work on water waves would have application to the study of radar scattering from free surfaces. The work on Ostwald ripening provides more detailed inf ormation on the state of materials whose manufacture depends on phase transitions.
