Twist vortices and their instabilities in the Taylor–Couette system

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Abstract
The problem of three-dimensional flows arising from the twist instability of Taylor vortices is investigated numerically in the narrow gap limit of the Taylor–Couette system with nearly corotating cylinders. There are two types of twist vortices: those that do not deform the in– and outflow boundaries of the Taylor vortices and those that do. The latter type are called wavy twist vortices and correspond to class II of Nagata (1986). The stability of the twist vortices with respect to arbitrary infinitesimal disturbances is analysed with the result that the twist solutions are unstable within a large part of the parameter space with respect to Eckhaus and skewed-varicose-type instabilities. An analytical model is described which fits the numerical results on the transition from axisymmetric vortices to unstable twist solutions. The theoretical findings are compared with experimental observations.