Observations have been made on the onset of instability, and on the waveform both at onset and in the finite amplitude region for flows with closed nonrotationally symmetric streamlines. The effect of placing obstacles in the gap between concentric rotating circular cylinders is shown to depend primarily on the extent to which they modify the mean flow. The case of a square inner cylinder and circular outer cylinder is compared with the case of a circular inner cylinder and square outer cylinder. It is shown that the former arrangement, which is time‐dependent, is much less stable than the latter. It is concluded that the shape of the boundaries in the Taylor double cylinder problem do not influence the stability markedly, other than by defining the clearance ratio, unless they make the problem time‐dependent.