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On stability of Taylor vortices by fifth-order amplitude expansions

Published online by Cambridge University Press:  29 March 2006

P. M. Eagles
P. M. Eagles
Affiliation:
Department of Mathematics, The City University, St John Street, London, E.C.1
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Abstract

Davey, Di Prima & Stuart's (1968) double amplitude expansion for disturbances in flow between concentric cylinders is formulated in matrix notation. The stability of the secondary equilibrium (Taylor-vortex) flow is calculated using fifth-order terms in amplitude, and using the full equations rather than the small-gap approximation. Qualitative confirmation is found of instabilities to the Taylor-vortex flow to non-a.xisymmetric disturbances at about 10 % above the first critical Taylor number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 49 , Issue 3 , 15 October 1971 , pp. 529 - 550
Copyright
© 1971 Cambridge University Press

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References

Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech., 21, 385–425.Google Scholar
Davey, A. 1962 The growth of Taylor vortices in flow between rotating cylinders. J. Fluid Mech., 14, 336–68.Google Scholar
Davey, A., Di Prima, R. C., & Stuart, J. T. 1968 On the instability of Taylor vortices. J. Fluid Mech., 31, 17–52.Google Scholar
Krueger, E. R., Gross, A. & Di Prima, R. C. 1966 On the relative importance of Taylor vortex and non-axisymmetric modes in flow between rotating cylinders. J. Fluid Mech., 24, 521–538.Google Scholar
Matkowsky, B. S. 1970 Nonlinear dynamic stability: a formal theory. SIAM J. Appl. Mach., 18, 872–883.Google Scholar
Reynolds, W. C. & Potter, M. C. 1967 Finite amplitude instability of parallel shear flows. J. Fluid Mech., 27, 465–492.Google Scholar
Schwarz, K. W., Springett, B. E. & Donnelly, R. J. 1964 Modes of instability in spiral flow between rotating cylinders. J. Fluid Mech., 20, 281–289.Google Scholar