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The Complex Spatiotemporal Dynamics of a Shallow Fluid Layer

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dc.contributor.authorO'Connor, Nicholas L.en
dc.contributor.committeechairPaul, Mark R.en
dc.contributor.committeememberTafti, Danesh K.en
dc.contributor.committeememberIliescu, Traianen
dc.contributor.departmentMechanical Engineeringen
dc.date.accessioned2014-03-14T20:36:38Zen
dc.date.adate2008-06-05en
dc.date.available2014-03-14T20:36:38Zen
dc.date.issued2008-05-05en
dc.date.rdate2008-06-05en
dc.date.sdate2008-05-13en
dc.description.abstractThe nonlinear and chaotic dynamics of a shallow fluid layer are investigated numerically using large-scale parallel numerical simulations. Two particular situations are studied in detail. First, a fluid layer is placed between rigid boundaries and heated from below to yield the chaotic dynamics of thermal convection rolls (Rayleigh-Bénard convection). Second is a free-surface fluid layer placed on a shaker to yield nonlinear surface waves (Faraday waves). In both cases the full governing partial differential equations are solved using parallel spectral element methods. Rayleigh-Bénard convection is studied in a cylindrical dish with realistic boundaries. The complete flow field is obtained as well as the spectrum of Lyapunov exponents and Lyapunov vectors. The Lyapunov exponents and their corresponding perturbation fields are used to determine when and where events occur that contribute most to the chaotic dynamics. Roll pinch-off and roll mergers are found to be the largest contributors. Two dimensional and three dimensional Faraday waves are studied with periodic boundary conditions. The full Navier-Stokes equations are solved including the complex dynamics of the free surface waves to gain a better understanding of the interplay between the viscous boundary layers, the nonlinear streaming flow, and the bulk flow. The vortices in the bulk flow are weak compared to the flow in the viscous boundary layers. The surface waves are found to be non-sinusoidal and the time evolution of the waves are explored for both large and small amplitude waves.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-05132008-133825en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05132008-133825/en
dc.identifier.urihttp://hdl.handle.net/10919/32705en
dc.publisherVirginia Techen
dc.relation.haspartThesis_Nick_OConnor.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectBoussinesqen
dc.subjectSpatiotemporalen
dc.subjectChaosen
dc.titleThe Complex Spatiotemporal Dynamics of a Shallow Fluid Layeren
dc.typeThesisen
thesis.degree.disciplineMechanical Engineeringen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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