Abstract
The very reliable and efficient numerical methods of [8, 11] were used for investigating axisymmetric steady Taylor vortex flows between concentric cylinders with periodic boundary conditions. The Reynolds number Re and period λ were continuously varied for fixed radius ratio η = 0.727. The basic (n, 2n) fold was found to exist up to at least Re = 4.6Re er(T = 21T cr). A large multiplicity of solutions (≥ 21 for λ = 2.5) and of fold points (≥ 25) and period doubling and tripling bifurcations were detected for Re = 3.65Re cr, η = 0.727, λ varying. Solutions with unusual flow patterns are displayed.
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References
Burkhalter, J. E. and Koschmieder, E. L. (1974) Steady supercritical Taylor vortices after sudden starts. Phys. Fluids 17, 1929–1935
Busse, F. H. and Or, A. C. (1986) Subharmonic and asymmetric convection rolls. ZAMP 37, 608–623; and Busse, F. H. Transition to asymmetric convection rolls. These proceedings
Busse, F. H. (1978) private communication
Dinar, N. and Keller, H. B., Computations of Taylor vortex flows using multigrid continuation methods. To be published
Eilbeck, J. C. Numerical study of bifuraction in a reaction diffusion model using pseudospectral and path following methods. These proceedings
Frank, G. and Meyer-Spasche, R. (1981) Computation of transitions in Taylor vortex flows. ZAMP 32, 710–720
Jones, C. A. (1981) Nonlinear Taylor vortices and their stability. JFM 102, 249–261
Keller, H. B. (1977) Numerical solution of bifurcation and nonlinear eigenvalue problems. In: Applications of Bifurcation Theory (ed. P. Rabinowitz), 359–384
Ladyženskaya, O. A. (1969) The mathematical theory of viscous incompressible flow. (Russian) Akademie Verlag, Gordon and Breach
Meyer-Spasche, R. and Keller, H. B. (1980) Computations of the axisymmetric flow between rotating cylinders. J. Comp. Phys. 35, 100–109
Meyer-Spasche, R. and Keller, H. B. (1985) Some bifurcation diagrams for Taylor vortex flows. Phys. Fluids 28, 1248–1252
Riecke, H. and Paap, H.-G. (1986) Stability and wave vector restriction of axisymmetric Taylor vortex flow. Phys. Rev. A 33, 547
Schreiber, I. and Kubiček, M. (1984) private communication
Temam, R. (1983) Navier-Stokes equations and nonlinear functional analysis. SIAM Philadelphia
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© 1987 Birkhäuser Verlag Basel
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Meyer-Spasche, R., Wagner, M. (1987). Steady Axisymmetric Taylor Vortex Flows with Free Stagnation Points of the Poloidal Flow. In: Küpper, T., Seydel, R., Troger, H. (eds) Bifurcation: Analysis, Algorithms, Applications. ISNM 79: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 79. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7241-6_23
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DOI: https://doi.org/10.1007/978-3-0348-7241-6_23
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7243-0
Online ISBN: 978-3-0348-7241-6
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