Strong exchange of stabilities in rapidly rotating parabolic Poiseuille flow

Poiseuille flow between two coaxial cylindrical pipes, with inner pipe translating at just the rate so that the velocity is parabolic, is rotated around the common axis of symmetry, with a common angular velocity. If the rotation rate is very large and it is assumed that the wave length of the critical disturbances is small, the governing equations take an approximate form that is analogous, remarkably, to Couette flow between coaxial cylinders with a certain difference. It is proved that if the rotation rate meets this criterion, the strong principle of exchange of stabilities (PES) holds; that is, all eigenvalues are real, and there is a first unstable eigenvalue. From a physical viewpoint, the resulting unstable motion initially takes the form of steady spiral vortices.