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Stability analysis of homogeneous shear flow : the linear and nonlinear theories and a Hamiltonian formulation

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dc.contributor.advisor Mahrt, Larry
dc.creator Hagelberg, Carl R.
dc.date.accessioned 2012-04-30T21:09:07Z
dc.date.available 2012-04-30T21:09:07Z
dc.date.copyright 1989-10-17
dc.date.issued 1989-10-17
dc.identifier.uri http://hdl.handle.net/1957/28933
dc.description Graduation date: 1990 en_US
dc.description.abstract The stability of steady-state solutions of the equations governing two-dimensional, homogeneous, incompressible fluid flow are analyzed in the context of shear-flow in a channel. Both the linear and nonlinear theories are reviewed and compared. In proving nonlinear stability of an equilibrium, emphasis is placed on using the stability algorithm developed in Holm et al. (1985). It is shown that for certain types of equilibria the linear theory is inconclusive, although nonlinear stability can be proven. Establishing nonlinear stability is dependent on the definition of a norm on the space of perturbations. McIntyre and Shepherd (1987) specifically define five norms, two for corresponding to one flow state and three to a different flow state, and suggest that still others are possible. Here, the norms given by McIntyre and Shepherd (1987) are shown to induce the same topology (for the corresponding flow states), establishing their equivalence as norms, and hence their equivalence as measures of stability. Summaries of the different types of stability and their mathematical definitions are presented. Additionally, a summary of conditions on shear-flow equilibria under which the various types of stability have been proven is presented. The Hamiltonian structure of the two-dimensional Euler equations is outlined following Olver (1986). A coordinate-free approach is adopted emphasizing the role of the Poisson bracket structure. Direct calculations are given to show that the Casimir invariants, or distinguished functionals, are time-independent and therefore are conserved quantities in the usual sense. en_US
dc.language.iso en_US en_US
dc.subject.lcsh Shear flow en_US
dc.subject.lcsh Hamiltonian systems en_US
dc.title Stability analysis of homogeneous shear flow : the linear and nonlinear theories and a Hamiltonian formulation en_US
dc.type Thesis/Dissertation en_US
dc.degree.name Master of Science (M.S.) in Atmospheric Sciences en_US
dc.degree.level Master's en_US
dc.degree.discipline Oceanic and Atmospheric Sciences en_US
dc.degree.grantor Oregon State University en_US
dc.description.digitization File scanned at 300 ppi (Monochrome) using ScandAll PRO 1.8.1 on a Fi-6670 in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR. en_US
dc.description.peerreview no en_us

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