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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
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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

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References

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