Show simple item record

dc.contributor.advisorNicholls, David Peter
dc.creatorNgom, Marieme
dc.date.accessioned2019-08-06T14:24:59Z
dc.date.available2019-08-06T14:24:59Z
dc.date.created2019-05
dc.date.issued2019-04-12
dc.date.submittedMay 2019
dc.identifier.urihttp://hdl.handle.net/10027/23752
dc.description.abstractThis thesis focuses on the well-posedness and stability of the Water Wave Equation in the context of the Faraday wave experiment. We prove that the solutions to the viscous water wave equation formulated by Dias, Dyachenko and Zakharov (DDZ) and supplemented with viscosity, surface tension and small vertical forcing is well-posed. We then derive some numerical stability results in the case of larger forcing and solve these equations numerically by using High Order Perturbation of Surfaces (HOPS) methods. We validate our code by first testing it in the case of traveling waves where exact solutions can be derived and by testing our approach against methods present in the literature.
dc.format.mimetypeapplication/pdf
dc.subjectFaraday Wave Experiment, Numerical Analysis, Partial Differential Equations, Field Expansions, Fluid Dynamics, Water Waves
dc.titleA Theoretical and Numerical Analysis of the Faraday Wave Experiment
dc.typeThesis
thesis.degree.departmentMathematics, Statistics and Computer Science
thesis.degree.grantorUniversity of Illinois at Chicago
thesis.degree.levelDoctoral
thesis.degree.namePhD, Doctor of Philosophy
dc.contributor.committeeMemberAwanou, Gerard
dc.contributor.committeeMemberDai, Mimi
dc.contributor.committeeMemberNenciu, Irina
dc.contributor.committeeMemberLiang, Jie
dc.type.materialtext
dc.contributor.chairNicholls, David Peter


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record