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Abstract
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| Highly resolved, accurate solutions of the two-dimensional incompressible Navier-Stokes and continuity equations, describing the evolution of a counter-rotating pair of vortices, have been obtained efficiently by spectral collocation and an eigenvalue decomposition algorithm. Such solutions have formed the basic state for subsequent three-dimensional BiGlobal eigenvalue problem (EVP) linear instability analyses, which monitor the modal response of the vortical systems to small-amplitude perturbations along the homogeneous axial spatial direction, without the need to invoke an assumption of azimuthal spatial homogeneity. A finite-element methodology (FEM) has been adapted to study instability of vortical flows and has been validated on the Batchelor vortex. Subsequently, instability of the counter-rotating pair of vortices obtained previously has been analyzed; essential to the success of the analysis has been the appropriate design of a calculation mesh, as well as exploitation of the symmetries of the basic state. The spatial structure of the amplitude functions of all unstable eigenmodes reflects the inhomogeneity of the basic state in the azimuthal spatial direction, thus providing a-posteriori justification for the use of the BiGlobal EVP concept. | |
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International
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Si |
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Congress
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AIAA Paper 2007-4359, 37th AIAA Fluid Dynamics Conference and Exhibit |
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960 |
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Place
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Miami, FL, USA |
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Reviewers
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Si |
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ISBN/ISSN
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ISBN-10: 1-56347-897 |
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Start Date
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25/06/2007 |
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End Date
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28/06/2007 |
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