Modulated Taylor–Couette flow

Abstract

The onset of instability in temporally modulated Taylor-Couette flow is considered. Critical Reynolds numbers have been found by computing Floquet exponents. We find that frequency modulation of the inner cylinder introduces a small destabilization, in agreement with the narrow-gap theory of Hall and some recent experiments of Ahlers. We review the previous computational literature on this problem, and find a number of contradictory results: the source of these discrepancies is examined, and a satisfactory resolution is achieved. Nonlinear axisymmetric calculations on the modulated problem have been done with an initial value code using a spectral method with collocation. The results are compared satisfactorily with Ahlers' measurements.At low modulation frequency, a large destabilization has been observed in past experiments. We show that this cannot be explained on the basis of perfect bifurcation theory: an analysis of the modulated amplitude equation shows that very small imperfections can substantially affect the behaviour at low frequency by giving rise to ‘transient’ vortices at subcritical Reynolds number. We argue that these ‘transient’ vortices are the source of the large destabilization seen in some experiments. Modelling the imperfections in the initial-value code provides additional confirmation of this effect.