Abstract.The eigenvalue problem for the linear stability of Couette flow between two rotating concentric cylinders to axisymmetric disturbances is considered. It is proved that the principle of exchange of stabilities holds when the cylinders rotate in the same direction and the circulation decreases outwards. The proof is based on the notion of a positive operator which is analogous to a positive matrix. Such operators have a spectral property which implies the principle of exchange of stabilities.

The problem of a steady motion of a viscous incompressible fluid between two Ž . rotating coaxial cylinders Couette flow is considered. It is shown by operator theory that it is linearly stable with respect to two dimensional disturbances under all circumstances. The proof is based on a lemma which can be generalized to apply to other problems with a similar structure.