Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T18:34:53.909Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability analysis of rotational Couette flow of stratified fluids

Published online by Cambridge University Press:  29 March 2006

E. M. Withjack  and
C. F. Chen
E. M. Withjack
Affiliation:
Mechanical, Industrial and Aerospace Engineering Department, Rutgers University, New Brunswiclr, New Jersey 08903 Present address : Transportation Systems Center, Cambridge, Mass.
C. F. Chen
Affiliation:
Mechanical, Industrial and Aerospace Engineering Department, Rutgers University, New Brunswiclr, New Jersey 08903
Get access Rights & Permissions [Opens in a new window]

Abstract

A linear stability analysis is used to investigate the stability of rotational Couette flow of sbratified fluids. The linearized time-dependent perturbation equations are solved using explicit finite-difference approximations. Small random axisymmetric perturbations of a given wavelength are initially distributed in the flow field, and their development in time is obtained by numerical integration. It is found that the kinetic energy of the perturbations oscillates in time owing to the periodic transformation of the disturbance flow field from a one-vortex system to a two-vortex system and vice versa. The neutral condition is defined as the state in which the maxima of the perturbation kinetic energy curve no longer change in time. A neutral-stability curve is obtained using the experimentally observed critical wavelengths. It is in general agreement with the experimental data, and it confirms the experimental result that stable density stratification enhances stability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 68 , Issue 1 , 11 March 1975 , pp. 157 - 175
Copyright
© 1975 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
Harris, D. L. & Reid, W. D. 1964 On the stability of viscous flow between rotating cylinders. Part 2. Numerical analysis. J. Fluid Mech. 20, 95.Google Scholar
Keller, H. B. 1968 Numerical Methods for Two-point Boundary- T'aZue Problems. Walthain, Massachusetts: Blaisdell.
Krueger, E. R., Gross, A. & Diprima, R. C. 1966 On the relative importance of Taylor-vortex and non-axisymmetric modes in flow between rotating cylinders. J. Fluid Mech. 24, 521.Google Scholar
Liu, D. C. & Chen, C. F. 1973 Numerical experiments on time-dependent rotational Couette flow. J. Fluid illech. 59, 77.Google Scholar
Snyder, H. A. 1968 Stability of rotating Couette flow. 11. Comparison with numerical results. Phys. fluids, 11, 1599.Google Scholar
Sparrow, E. M., Munro, W. D. & Jonsson, V. K. 1964 Instability of the flow between rotating cylinders: the wide-gap problem. J. Fluid Mech. 20, 35.Google Scholar
Walowit, J., Tsao, S. & Diprima, R. C. 1964 Stability of flow between arbitrarily spaced concentric cylindrical surfaces including the effect of a radial temperature gradient. J. Appl. Mech. 31, 585.Google Scholar
Withjack, E. M. & Chen, C. F. 1974 An experimental study of Couette instability of stratified fluids. J. Fluid Mech. 66. 725.Google Scholar