Taylor vortex flow is one of the basic problems of nonlinear hydrodynamic stability. In contrast with the wide region of wavenumber predicted by the linear theory, experiments show that Taylor vortex flow only appears in a small region containing the critical wavenumber ß<sub>er</sub> This phenomenon is called wave selection. In this work, several high-order perturbation methods and a numerical method are established. Both evolution and steady state of the How caused by single or several disturbances are studied. The existence of multiple steady states for disturbances with small wavenumber is discovered and proved. The stable and unstable steady state solutions and some associated phenomena such as jump phenomenon and hysteresis phenomenon are found. and explained. In the small region, the wavenumbers and initial amplitudes of disturbances determine the wavenumber of the flow. But outside this region, only the wavenumbers of the disturbances have effect on the wave selection. These results indicate that unstable solutions play a key role in wave selection. The side-band stability curve produced by the high-order perturbation methods is accurate at low Taylor numbers but incorrect at relatively high Taylor numbers. The relation of the unstable solutions and side-band stability is discussed. Besides, the overshoot and the oscillation phenomena during evolution are studied in detail. Connections between this work and experiments are discussed. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/53628 |
| Date | January 1986 |
| Creators | Li, Rihua |
| Contributors | Engineering Mechanics, Herbert, Thorwald, Johnson, Lee W., Meirovitch, Leonard, Mook, Dean T., Smith, C.W. |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | v, 169 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 13912557 |
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