Stability of power law fluid flow between rotating cylinders

The centrifugal instability of power law fluid flow when the fluid fills the gap between two rotating concentric cylinders of infinite length is addressed. The instability of the circular Couette flow is determined via linear stability analysis. In the narrow gap case, the critical Taylor number is determined analytically, while in the general gap case, a finite-difference numerical method is employed. The results are shown to be in agreement with existing theoretical and experimental findings. The super-critical flow is investigated by means of a weakly non-linear analysis method. The Taylor-vortex flow (the secondary stable flow) is obtained. The instability of this flow is determined as we present the critical Taylor number when the Taylor vortices begin to exhibit a waviness in the azimuth