Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-11T10:29:45.832Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of circular Couette flow with variable inner cylinder speed

Published online by Cambridge University Press:  20 April 2006

G. P. Neitzel
G. P. Neitzel
Affiliation:
Department of Mechanical and Energy Systems Engineering. Arizona State University, Tempe, AZ 85287
Get access Rights & Permissions [Opens in a new window]

Abstract

Energy & ability theory is employed to study the finite-amplitude stability of a viscous incompressible fluid occupying the space between a pair of concentric cylinders when the inner-cylinder angular velocity varies linearly with time. For the case with a fixed outer cylinder and increasing inner-cylinder speed, we find an enhancement of stability, consistent with a linear-theory result due to Eagles. When the inner-cylinder speed decreases, we find an initially decreased stability bound, indicating the possibility of hysteresis, while, if the inner cylinder is allowed to reverse direction and linearly increase in speed, we find significant stability enhancement.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 123 , October 1982 , pp. 43 - 57
Copyright
© 1982 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

Chen, C. F. & Kirchner, R. P. 1971 Stability of time-dependent rotational Couette flow. Part 2. Stability analysis. J. Fluid Mech. 48, 365.Google Scholar
Chen, C. F., Liu, D. C. S. & Skok, M. W. 1973 Stability of circular Couette flow with constant finite acceleration. Trans. A.S.M.E. E: J. Appl. Mech. 40, 347.Google Scholar
Chen, J.-C. & Neitzel, G. P. 1982 Strong stability of impulsively initiated Couette flow for both axisymmetric and non-axisymmetric disturbances. Trans. A.S.M.E. E: J. Appl. Mech. (to appear).Google Scholar
Di Prima, R. C. & Swinney, H. L. 1981 Instabilities and transition in flow between concentric rotating cylinders. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub), p. 139. Springer.
Eagles, P. M. 1977 On the stability of slowly-varying flow between concentric cylinders. Proc. R. Soc. Lond. A 355, 209.Google Scholar
Hall, P. 1975 The stability of unsteady cylinder flows. J. Fluid Mech. 67, 29.Google Scholar
Homsy, G. M. 1973 Global stability of time-dependent flows: impulsively heated or cooled fluid layers. J. Fluid Mech. 60, 129.Google Scholar
Liu, D. C. S. & Chen, C. F. 1973 Numerical experiments on time-dependent rotational Couette flow. J. Fluid Mech. 59, 77.Google Scholar
Neitzel, G. P. 1982 Marginal stability of impulsively initiated Couette flow and spin-decay. Phys. Fluid. 25, 226.Google Scholar
Neitzel, G. P. & Davis, S. H. 1980 Energy stability theory of decelerating swirl flows. Phys. Fluids 23, 432.Google Scholar
Park, K., Crawford, G. L. & Donnelly, R. J. 1981 Determination of transition in Couette flow in finite geometries. Phys. Rev. Lett. 47, 1448.Google Scholar
Riley, P. J. & Laurence, R. L. 1976 Linear stability of modulated circular Couette flow. J. Fluid Mech. 75, 625.Google Scholar
Seminara, G. & Hall, P. 1975 Linear stability of slowly-varying unsteady flows in a curved channel. Proc. R. Soc. Lond. A 346, 279.Google Scholar
Serrin, J. 1959 On the stability of viscous fluid motions. Arch. Rat. Mech. Anal. 3, 1.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289.Google Scholar
Tustaniwskyj, J. I. & Carmi, S. 1980 Nonlinear stability of modulated finite gap Taylor flow. Phys. Fluids 23, 1732.Google Scholar