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dc.rights.licenseRestricted to current Rensselaer faculty, staff and students. Access inquiries may be directed to the Rensselaer Libraries.
dc.contributorHerron, Isom H., 1946-
dc.contributorSiegmann, W. L.
dc.contributorMcLaughlin, Joyce
dc.contributorHirsa, Amir H.
dc.contributor.authorEckhardt, Daniel Q.
dc.date.accessioned2021-11-03T08:38:49Z
dc.date.available2021-11-03T08:38:49Z
dc.date.created2016-09-27T14:07:38Z
dc.date.issued2016-08
dc.identifier.urihttps://hdl.handle.net/20.500.13015/1744
dc.descriptionAugust 2016
dc.descriptionSchool of Science
dc.description.abstractThis work also demonstrates techniques for handling global phenomenon in the 3D Boussinesq equations on a semi-infinite domain; by considering the problem of rotating Rayleigh-Bènard convection; with non-periodicity in the y-axis, and with a semi-infinite geometry. For this problem, the absence of a periodic cell and the added boundary makes the techniques previously available for analyzing this flow unusable. Hence, a rigorous method is derived; and this uses a weighted generalized Lyapunov functional in a Sobolev embedded space, to show that rotation has a stabilizing effect on this flow. A weighted Toroidal-Poloidal decomposition is also considered as a more tractable approach for handling this type of problem.
dc.description.abstractMagnetorotational Instability (MRI) is of great importance to astrophysics, as it is theorized to be the accretion driving phenomenon in accretion disks in astrophysical flows, for example, around black holes. Though MRI has long been known, it has yet to be observed at in laboratory experiments, partly due to the difficulty of creating the exact conditions in accretion disks. MRI can be studied by considering magnetized Taylor-Couette flow in a hydrodynamically stable regime according to the Rayleigh criterion. However, it is shown here that MRI is in fact suppressed when the term representing the twisting of radial magnetic components into azimuthal ones is dropped, and that no other instabilities occur, even with Navier-slip and conducting boundary conditions, as opposed to no-slip and insulating boundaries. A generalized Lyapunov functional is proposed to study the global stability behavior in this type of flow.
dc.language.isoENG
dc.publisherRensselaer Polytechnic Institute, Troy, NY
dc.relation.ispartofRensselaer Theses and Dissertations Online Collection
dc.subjectMathematical sciences
dc.titleMagnetorotational instability suppression and Rayleigh-Bènard convection in a semi-infinite layer
dc.typeElectronic thesis
dc.typeThesis
dc.digitool.pid177457
dc.digitool.pid177458
dc.digitool.pid177459
dc.rights.holderThis electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
dc.description.degreePhD
dc.relation.departmentDept. of Mathematical Sciences


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