The energy stability analysis for an arbitrary gap time-dependent flow is performed. The solution for the basic flow is obtained assuming that either one or both cylinders rotate with a mean and/or sinusoidal velocity. Arbitrary finite amplitude three-dimensional disturbances are considered with two-dimensional axisymmetric disturbances found to render the smallest eigenvalues. The energy stability limits are found to be strongly dependent on the gap size as well as on the modulation frequency.
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Tustaniwskyj et al. (1980) studied this question.
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