On the relative importance of Taylor-vortex and non-axisymmetric modes in flow between rotating cylinders

Abstract

The small-gap equations for the stability of Couette flow with respect to non-axisymmetric disturbances are derived. The eigenvalue problem is solved by a direct numerical procedure. It is found that there is a critical value of Ω2/Ω1(Ω1, Ω2 and R1, R2 are the angular velocities and radii of the inner and outer cylinders respectively) of approximately −0·78, above which the critical disturbance is axisymmetric and below which it is non-axisymmetric. In particular for R1/R2 = 0·95, Ω2/Ω1 = −1, the wave-number in the azimuthal direction of the critical disturbance is m = 4. This result is confirmed when the full linear disturbance equations are considered, i.e. the small-gap approximation is not made.