Complex eigenvalues for the stability of Couette flow
Abstract
The eigenvalue problem for the linear stability of Couette flow between rotating concentric cylinders to axisymmetric disturbances is considered. It is shown by numerical calculations and by formal perturbation methods that when the outer cylinder is at rest there exist complex eigenvalues corresponding to oscillatory damped disturbances. The structure of the first few eigenvalues in the spectrum is discussed. The results do not contradict the principle of exchange of stabilities, namely, for a fixed axial wavenumber the first mode to become unstable as the speed of the inner cylinder is increased is nonoscillatory as the stability boundary is crossed.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 November 1984
 DOI:
 10.1098/rspa.1984.0109
 Bibcode:
 1984RSPSA.396...75D
 Keywords:

 Computational Fluid Dynamics;
 Concentric Cylinders;
 Couette Flow;
 Eigenvalues;
 Flow;
 Flow Stability;
 Rotating Cylinders;
 Taylor Instability;
 Adjoints;
 Angular Velocity;
 Boundary Value Problems;
 Flow Velocity;
 Perturbation Theory;
 Fluid Mechanics and Heat Transfer