Finite-amplitude modulated Taylor-Couette flow

Abstract

The Taylor-Couette flow with finite-amplitude modulated cylinders is examined in this study. A spectral/finite-difference approach is used based on domain transformation. The governing equations are mapped over the rectangular domain, and the flow field is represented spectrally in the axial direction, which, together with the Galerkin projection, led to a system of equations that are solved using a variable step finite-difference discretization. The vortex formation and pattern selection are examined after the validity of the method is established. The inner and outer cylinders are modulated in phase, and are free to co- or counter-rotate at different speed. It is found that the presence of modulation leads to the emergence of steady vortex flow even at vanishingly small Taylor number. The vortex structure is found to have the same periodicity as the forcing, even after the critical Taylor number corresponding to the onset of vortex flow straight cylinders is exceeded. The outer to inner cylinder velocity ratio controls not only the vortex strength and the nonlinearity but also the size, location, and breakup of the vortices. It is also found that the forcing wave number that generates the most intense vortex flow varies slightly with Ta and is different from the critical wave number predicted by linear stability analysis for straight cylinders.