Phase velocity and group velocity of waves in Taylor-Couette flow

The Taylor-Couette flow between two concentric cylinders have been studied extensively in the fluid dynamics literature. Taylor-Couette flow is very important in fluid dynamics since it is simple and at the same time it displays all the regimes in general fluid flow. It is observed in the Taylor-Couette flow that for low Reynolds number static vortices are formed and when the Reynolds number crosses a threshold, waves are formed in the form of wavy vortex flow around the cylinder. This phenomenon is surprising and the formation of the waves have been studied experimentally and computationally using standard computational fluid dynamics software. However, no analytical expression for the speed of the waves have been arrived at. In this article, exact expressions for the phase velocity and group velocity of the waves in Taylor-Couette flow have been arrived at when both the cylinders are rotating at the same angular speed. Also, it has been shown in this work that the waves are in general transverse, damped and circularly polarized which corresponds very well to experimental studies.