Some Boundary-Value Problems for Water Waves

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Some Boundary-Value Problems for Water Waves

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Title: Some Boundary-Value Problems for Water Waves
Author: Vasan, Vishal
Abstract: Euler's equations describe the evolution of waves on the surface of an ideal incompressible fluid. In this dissertation, I discuss some boundary-value problems associated with Euler's equations. My approach is motivated by the ideas generated by Fokas and collaborators, particularly the notion of a global relation for boundary-value problems for partial differential equations. I introduce a new method to compute the evolution of the free surface of a water wave based on a reinterpretation of the relevant global relation. Next I consider the bathymetry reconstruction problem <italic>i.e.<\italic>, the reconstruction of the bottom boundary of a fluid from measurements of the free-surface elevation alone. By analyzing the global relation for the water-wave problem, I derive an exact, fully nonlinear equation which is solved for the bottom boundary. Finally, I present a method of reconstructing the free surface of a water wave using measurements of the pressure at the bottom boundary. Using this reconstruction, I obtain several new asymptotic approximations of the surface elevation in terms of the pressure at the bottom. Comparisons with numerical and experimental data show excellent agreement with my predicted reconstructions.
Description: Thesis (Ph.D.)--University of Washington, 2012
URI: http://hdl.handle.net/1773/20723
Author requested restriction: No embargo

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