Bifurcation analysis in laminar free-surface Taylor–Couette flow
Title: Bifurcation analysis in laminar free-surface Taylor–Couette flow
SNIC Project: SNIC 2021/22-728
Project Type: SNIC Small Compute
Principal Investigator: Prabal Negi <>
Affiliation: NORDITA
Duration: 2021-09-22 – 2022-10-01
Classification: 20306


The Taylor-Couette flow has been a protoypical problem in pattern formation in fluid dynamics. Its stability was first studied by Taylor [1923] in the infinite cylinder setting, and later by Benjamin [1978] for finite cylinders with top and bottom walls. The problem is the hydrodynamic twin of the Rayleigh-Bénard Convection and has been studied in thousands of works. A slightly modified Taylor-Couette problem including gravitational effects with a free surface, on the other hand, has been almost ignored in the literature. The flow problem serves as a model problem for the appearance of gravity waves in rotating flows which are relevant to geophysical applications. In a turbulent setting, the flow is known to exhibit bistable states with hysteretic transitions between them The problem has also been suggested as a simpler model problem for a bathtub vortex, which is known to have surprisingly complex flow structures. Owing to the lack of focus on the problem in the literature, the precise boundary between the axi-symmetric states and the breaking of this symmetry is also not known precisely. Toya et al. [1994], Watanabe and Toya [2012] report bifurcated states of the Taylor-Couette problem with asymmetric boundary conditions but, primarily for axisymmetric bifurcations leading to Taylor vortices. The axisymmetry breaking bifurcations have not been reported. Moreover, the studies have also been confined to a limited range of aspect ratios. Accordingly, the current work aims to investigate the instabilities of the laminar free-surface Taylor-Couette flow over a range of different parameters, with particular emphasis on establishing the emergence of azimuthal symmetry breaking.