Linear stability analysis of fully developed axisymmetric steady spatially modulated Taylor–Couette flow (TCF) is carried out in the narrow-gap limit. In contrast to unforced TCF, only the vortical base flow is possible in the forced case. It is found that the forcing tends to generally destabilize the base flow, especially around the critical point corresponding to unforced flow. Both the critical Taylor number and wave number are found to essentially linearly decrease with modulation amplitude.
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