The principle of exchange of stabilities for Couette flow
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.