Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-20T10:14:45.967Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow-history effect on higher modes in the spherical Couette system

Published online by Cambridge University Press:  26 April 2006

Koichi Nakabayashi  and
Yoichi Tsuchida
Koichi Nakabayashi
Affiliation:
Department of Mechanical Engineering, Nagoya Institute of Technology, Nagoya 466, Japan
Yoichi Tsuchida
Affiliation:
Department of Mechanical Engineering, Nagoya Institute of Technology, Nagoya 466, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

Our flow-visualization and spectral studies of spherical Couette flow between two concentric spheres with only the inner sphere rotating for the clearance ratio (or gap ratio) 0.14 where the Taylor instability occurs have been pursued to systematically explore how and why a variety of wavenumbers and rotation frequencies of the non-axisymmetric periodic disturbances occurs at the same supercritical Reynolds number. The observed periodic disturbances constitute six kinds of disturbances: spiral TG (Taylor–Görtler) vortices, twists developing within toroidal TG vortices, both unmodulated and modulated waves travelling on the TG vortices, and both Stuart vortices and shear waves developing within the Ekman-type secondary flow. Development of these disturbances depends strongly on the flow mode at the initial Reynolds number (initial flow mode) and on the Reynolds-number evolution process approaching the final Reynolds number (acceleration rate and history of the Reynolds number). In our previous studies (Nakabayashi 1983; Nakabayashi & Tsuchida 1988 a, b), we clarified the structures, wavenumbers and rotation frequencies of the periodic disturbances caused by a quasi-static increasing of the Reynolds number. In the present study, we consider how the characteristics of periodic disturbances depend on the following three factors: (i) the rate of increase of the Reynolds number; (ii) the number of toroidal vortices in an initial flow mode; and (iii) the quasi-static Reynolds-number history. The flow modes observed in the present study are all stable to small perturbations, and the transitions among the flow modes are reproducible.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 295 , 25 July 1995 , pp. 43 - 60
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andereck, C. D., Dickman, R. & Swinney, H. L. 1983 New flows in a circular Couette system with co-rotating cylinders. Phys. Fluids 26, 1395.Google Scholar
Bartels, F. 1982 Taylor vortices between two concentric rotating spheres. J. Fluid Mech. 119, 1.Google Scholar
Bonnet, J. P. & Alziary de Roquefort, T. 1976 Ecoulement entre deux sphères concentriques en rotation. J. Méc. 15, 373.Google Scholar
Bühler, K. 1990 Symmetric and asymmetric Taylor vortex flow in spherical gaps. Acta Mechanica 81, 3.Google Scholar
Bühler, K. & Zierep, J. 1987 Dynamical instabilities and transition to turbulence in spherical gap flows. In Advances in Turbulence, Proc. 1st European Turbulence Conf. (ed. G. Comte-Bellot & J. Mathieu), p. 16. Springer.
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385.Google Scholar
Dennis, S. C. R. & Quartapelle, L. 1984 Finite difference solution to the flow between two rotating spheres. Computers Fluids 12, 77.Google Scholar
Gorman, M. & Swinney, H. L. 1982 Spatial and temporal characteristics of modulated waves in the circular Couette system. J. Fluid Mech. 117, 123.Google Scholar
King, G. P., Li, Y., Lee, W., Swinney, H. L. & Marcus, P. S. 1984 Wave speeds in wavy Taylor-vortex flow. J. Fluid Mech. 141, 365.Google Scholar
Marcus, P. S. 1984a Simulation of Taylor–Couette flow. Part 1. Numerical methods and comparison with experiment. J. Fluid Mech. 146, 45.Google Scholar
Marcus, P. S. 1984b Simulation of Taylor–Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave. J. Fluid Mech. 146, 65.Google Scholar
Marcus, P. S. & Tuckerman, L. S. 1987a Simulation of flow between concentric rotating spheres. Part 1. Steady states. J. Fluid Mech. 185, 1.Google Scholar
Marcus, P. S. & Tuckerman, L. S. 1987b Simulation of flow between concentric rotating spheres. Part 2. Transitions. J. Fluid Mech. 185, 31.Google Scholar
Nakabayashi, K. 1983 Transition of Taylor–Görtler vortex flow in spherical Couette flow. J. Fluid Mech. 132, 209.Google Scholar
Nakabayashi, K. & Tsuchida, Y. 1988a Spectral study of the laminar–turbulent transition in spherical Couette flow. J. Fluid Mech. 194, 101.Google Scholar
Nakabayashi, K. & Tsuchida, Y. 1988b Modulated and unmodulated travelling azimuthal waves on the toroidal vortices in a spherical Couette system. J. Fluid Mech. 195, 495.Google Scholar
Newhouse, S., Ruelle, D. & Takens, F. 1978 Occurrence of Strange Axion A attractors near quasi-periodic flows on Tm, m > 3. Commun. Math. Phys. 64, 35.Google Scholar
Rand, D. 1982 Dynamics and symmetry, predictions for modulated waves in rotating fluids. Arch. Rat. Mech. Anal. 79, 1.Google Scholar
Sawatzki, O. & Zierep, J. 1970 Das Stromfeld im Spalt zwischen zwei konzentrischen Kugelflächen, von denen die innere rotiert. Acta Mechanica 9, 13.Google Scholar
Wimmer, M. 1976 Experiments on a viscous fluid flow between concentric rotating spheres. J. Fluid Mech. 78, 317.Google Scholar
Wimmer, M. 1988 Viscous flows and instabilities near rotating bodies. Prog. Aerospace Sci. 25, 43.Google Scholar
Yavorskaya, I. M., Belyaev, Yu. N., Monakhov, A. A., Astaf'eva, N. M., Scherbakov, S. A. & Vvedenskaya, N. D. 1980 Stability, nonuniqueness and transition to turbulence in the flow between two rotating spheres. Rep. 595. Space Research Institute of the Academy of Science, USSR.