Lord Rayleigh studied the stability of the problem with inviscid assumption i.e., perturbing Euler equations. The criterion states that in the absence of viscosity the necessary and sufficient condition for distribution of azimuthal velocity  to be stable is
everywhere in the interval; and, further, that the distribution is unstable if  should decrease anywhere in the interval. Since  represents angular momentum per unit mass, of a fluid element about the axis of rotation, an alternative way of stating the criterion is: a stratification of angular momentum about an axis is stable if and if only it increases monotonically outward. 
Applying this criterion to the Taylor-Couette flow indicates that the flow is stable if , i.e., for stability, the outer cylinder must rotate (in the same sense) with an angular speed greater than -times that of the inner cylinder. The Rayleighs criterion is violated () throughout the whole fluid when . On the other hand, when the cylinders rotate in opposite directions, i.e., when , Rayleighs criterion is violated only in the inner region, i.e.,  for  where .