In a seminal work, G. I. Taylor found the criterion for instability in the presence of viscous forces both experimentally and theoretically. In general, viscous forces are found to postpone the onset of instability, predicted by Rayleigh's criterion. The stability is characterized by three parameters, namely, ,  and a Taylor number 
The first result pertains to the fact that the flow is stable for , consistent with Rayleigh's criterion. However, there are also stable cases in certain parametric range for .
Taylor obtained explicit criterion for the narrow gap in which the annular gap  is small compared with the mean radius , or in other words, . A better definition of Taylor number in the thin-gap approximation is 
In terms of this Taylor number, the critical condition for same-sense rotation was found to be
As , the critical Taylor number is given by