Taylor–Couette system in the narrow-gap limit, revisited, with a corrigendum to the paper by Nagata (2023, Philosophical Transaction A.)

Source abstract

We study transition from circular Couette flow to Taylor–Couette flow in the narrow-gap limit. We find that subcritical bifurcations of a nonlinear axisymmetric flow occur at the linear critical point when the angular velocity ratio for the cylinders, μ , is less than approximately −0.5. We also demonstrate that two nonlinear axisymmetric flow branches with the same wavenumber as that for the critical mode exist for μ = 0 . Introducing the modified Taylor number τ , analyses for any μ < 1 are made possible, so that this study supplements the recent analysis of Nagata M. 2023 Taylor-couette flow in the narrow-gap limit. Philos. Trans. R. Soc. A 381, 20220134. (doi: 10.1098/rsta.2022.0134 ), in which the case μ = − 1 was excluded, because the critical value of the conventional Taylor number T a used therein approaches zero as μ → − 1 . The present analysis takes into account all the contributions from the inertia term, including a component which was neglected in [1]. The effect of the inclusion of this previously neglected component is surveyed at the end.