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dc.contributor.advisorDeconinck, Bernarden_US
dc.contributor.authorVasan, Vishalen_US
dc.date.accessioned2012-09-13T17:31:29Z
dc.date.available2012-09-13T17:31:29Z
dc.date.issued2012-09-13
dc.date.submitted2012en_US
dc.identifier.otherVasan_washington_0250E_10437.pdfen_US
dc.identifier.urihttp://hdl.handle.net/1773/20723
dc.descriptionThesis (Ph.D.)--University of Washington, 2012en_US
dc.description.abstractEuler'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.mimetypeapplication/pdfen_US
dc.language.isoen_USen_US
dc.rightsCopyright is held by the individual authors.en_US
dc.subjectBoundary-value problems; Inverse problems; Water wavesen_US
dc.subject.otherApplied mathematicsen_US
dc.subject.otherMathematicsen_US
dc.subject.otherApplied mathematicsen_US
dc.titleSome Boundary-Value Problems for Water Wavesen_US
dc.typeThesisen_US
dc.embargo.termsNo embargoen_US


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