The stability of flow in a Couette flow apparatus induced by the motion of the inner cylinder brought to its final speed through a constant finite acceleration is investigated both experimentally and theoretically. The instability of the flow manifests itself in the simultaneous occurrence of Taylor vortices more or less evenly spaced along the inner cylinder. A linear stability analysis using the initial-value problem approach is applied to this flow situation. Its prediction on the delay of the onset time of secondary flow and the increase in critical wavelength when the acceleration is reduced from infinite to finite values is generally confirmed by the experimental results.

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