Dynamics and Stability of Buoyancy-Induced Flows

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dc.contributor.advisorGrigo, Alexander
dc.contributor.advisorNikola, Petrov
dc.contributor.authorSheaib, Dania
dc.contributor.committeeMemberAlbert, John
dc.contributor.committeeMemberMarfurt, Kurt
dc.contributor.committeeMemberRemling, Christian
dc.date.accessioned2019-05-08T18:16:36Z
dc.date.available2019-05-08T18:16:36Z
dc.date.issued2019-05-10
dc.date.manuscript2019
dc.description.abstractThe present dissertation tackles two different problems in fluid mechanics. In the first problem, we study the stability of free or natural convection of a compressible fluid over a heated plate underlying a semi-infinite vertical slot and underlying a closed vessel. For both settings, we show linear and non-linear stability of the reference solution by constructing respective Lyapunov functions and using LaSalle's Invariance Principle. The construction of the Lyapunov function is motivated by the assumption that the fluid particles evolve according to a Markov chain. In the second problem, we study the flow dynamics of a viscous stably stratified fluid in a channel with time-periodic temperature variations applied at the sidewalls. Seeking solutions in the form of simple harmonic oscillations, we obtain analytical temperature and velocity profiles for the one-dimensional time-dependent flow. We then use these solutions to study the possibility of resonance of the fluid flow with the periodic oscillations of the externally supplied temperatures at the walls. Results indicate the existence of resonance depicted as prominent peaks of physical quantities at certain frequencies of the external temperature oscillations.en_US
dc.identifier.urihttps://hdl.handle.net/11244/319610
dc.languageenen_US
dc.subjectNavier-Stokes Equationsen_US
dc.subjectDynamicsen_US
dc.subjectStabilityen_US
dc.subjectBuoyancy-Induced Flowsen_US
dc.subjectNatural Convectionen_US
dc.subjectSteady Flowen_US
dc.subjectHorizontal Plateen_US
dc.subjectTime-dependent Flowen_US
dc.subjectVertical Channelen_US
dc.subjectStratified Fluiden_US
dc.subjectLyapunov Functionen_US
dc.subjectResonanceen_US
dc.subjectPrandtl Numberen_US
dc.thesis.degreePh.D.en_US
dc.titleDynamics and Stability of Buoyancy-Induced Flowsen_US
ou.groupCollege of Arts and Sciences::Department of Mathematicsen_US
shareok.orcid0000-0001-7427-3587en_US

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