On the transition of transient growth mechanism in Taylor–Dean flow

Abstract

We investigate optimal perturbation and its transient growth characteristics in Taylor–Dean flow theoretically. The parameter [Formula: see text], accounting for the ratio of average pumping velocity induced by azimuthal pressure gradient to rotating velocity by rotating cylinders, is varied from −5 to 5. The results show that for the rigid rotation case, the energy growth of optimal perturbation is increased with increasing magnitude of azimuthal pressure gradient. Further, both the main and secondary peak of the amplitude of azimuthal velocity are seen to be shifted towards the outer cylinder for wide gap case, and both are shifted oppositely towards the inner cylinder for narrow gap case. Viewing the time evolution of the energies in the three velocity components for wide gap case, anti-lift-up mechanism replaces lift-up mechanism as the dominant mechanism for energy growth, when [Formula: see text] changes from −5 to 5. While for narrow gap case, lift-up mechanism is always responsible for transient growth of axisymmetric perturbation, no matter how strong azimuthal pressure gradient is considered.