Stability of flow in torsional flow. Taylor determined the critical speed of rotation for flow between concentric cylinders with the inner cylinder rotating. The transition is characterized by a critical Taylor number, \(T a\), defined as

\[
T a=\frac{R_{\mathrm{o}}^{4} \kappa(1-\kappa)^{3}\left(\omega_{1}^{2}-\omega_{2}^{2}\right)}{v^{2}}
\]

The transition for only the inner cylinder rotating was obtained by Taylor as 1709 by performing a linear stability analysis. Set up a model and analyze this problem.