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Some Boundary-Value Problems for Water Waves

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dc.contributor.advisor Deconinck, Bernard en_US Vasan, Vishal en_US 2012-09-13T17:31:29Z 2012-09-13T17:31:29Z 2012-09-13 2012 en_US
dc.identifier.other Vasan_washington_0250E_10437.pdf en_US
dc.description Thesis (Ph.D.)--University of Washington, 2012 en_US
dc.description.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. en_US
dc.format.mimetype application/pdf en_US
dc.language.iso en_US en_US
dc.subject Boundary-value problems; Inverse problems; Water waves en_US
dc.subject.other Applied mathematics en_US
dc.subject.other Mathematics en_US
dc.subject.other Applied mathematics en_US
dc.title Some Boundary-Value Problems for Water Waves en_US
dc.type Thesis en_US
dc.embargo.terms No embargo en_US

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