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Spiral vortex flows of the counter-rotating Taylor–Couette system in the narrow-gap limit

Published online by Cambridge University Press:  08 October 2025

Masato Nagata Open the ORCID record for Masato Nagata [Opens in a new window]
Masato Nagata*
Affiliation:
Graduate School of Engineering, Kyoto University, Kyoto 615-8530, Japan
*
Corresponding author: Masato Nagata, nagata.masato.45x@st.kyoto-u.ac.jp
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Abstract

Finite-amplitude spiral vortex flows are obtained numerically for the Taylor–Couette system in the narrow limit of the gap between two concentric rotating cylinders. These spiral vortex flows bifurcate from circular Couette flow before axisymmetric Taylor vortex flow sets in when the ratio $\mu$ of the angular velocities of the outer to the inner cylinder is less than −0.78, consistent with the results of linear stability analysis by Krueger et al. (J. Fluid Mech., vol. 24, 1966, pp. 521–538), while the boundary of existence of spiral vortex flows is determined not by the linear critical point, but by the saddle-node point of the subcritical spiral vortex flow branch for $\mu \lessapprox -0.75$, when the axial wavenumber $\beta =2.0$. It is found that the nonlinear spiral vortex flows exhibit the mean flow in the axial direction as well as in the azimuthal direction, and that the profiles of both mean-flow components are asymmetric about the centre plane between the gap.

JFM classification

Instability: Taylor-Couette flow Nonlinear Dynamical Systems: Bifurcation Instability: Nonlinear instability

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JFM Papers
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Journal of Fluid Mechanics , Volume 1020 , 10 October 2025 , A53
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© The Author(s), 2025. Published by Cambridge University Press

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