The stability of viscous flow under an axial pressure gradient between two co-axial cylinders rotating in the same direction is considered. The critical Taylor number (T c) for the onset of instability is then a function of the Reynolds number (R) of the mean axial flow. A perturbation theory valid in the limit P-> 0 is developed and the formula Tc(B) = Tc(0) + 26.5P2 (R-> 0) is established.
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S. Chandrasekhar (1962) studied this question.