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dc.contributor.advisorDeconinck, Bernarden_US
dc.contributor.authorTrichtchenko, Olgaen_US
dc.date.accessioned2015-02-24T17:30:18Z
dc.date.submitted2014en_US
dc.identifier.otherTrichtchenko_washington_0250E_13964.pdfen_US
dc.identifier.urihttp://hdl.handle.net/1773/27391
dc.descriptionThesis (Ph.D.)--University of Washington, 2014en_US
dc.description.abstractWe analyze the stability of solutions to Euler's equations in the presence of surface tension. First we compute stationary solutions to periodic Euler's equations in a travelling frame of reference and then we analyze their spectral stability. Depending on the coefficient of surface tension, we see resonant effects in the solutions. This results in a myriad of instabilities for gravity-capillary waves. Since the theory for analyzing the stability of water waves is general to all Hamiltonian systems, we extend the results to other equations, mainly ones that are used to model water waves in different asymptotic regimes. We compare the stability results for the model equations to those we obtain for the full water wave system and comment on the applicability of these models.en_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_USen_US
dc.rightsCopyright is held by the individual authors.en_US
dc.subjectEuler's equations; Numerical methods; Stability; Water wavesen_US
dc.subject.otherApplied mathematicsen_US
dc.subject.otherapplied mathematicsen_US
dc.titleOn the instability of water waves with surface tension.en_US
dc.typeThesisen_US
dc.embargo.termsRestrict to UW for 1 year -- then make Open Accessen_US
dc.embargo.lift2016-02-24T17:30:18Z


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