Instability of the interface between two inviscid fluids inside a rotating annulus in the absence of gravity

In this paper we investigate the linear instability of two superposed inviscid fluids between two rotating concentric cylinders. In the hydrostatic state the two fluids rotate as a rigid body with the same angular velocity as the annulus. Two problems are investigated. First, calculations are made of the instability of the liquid layer coating the outside of a cylinder under rotation. Second, results are obtained of the instability of two stratified fluids between two concentric cylinders. The first case is the most unstable condition of the second case when the outer fluid is absent. Therefore, in the second case only the instability of a system with a heavier fluid located outside the interface was investigated. It was found that the introduction of the inner cylinder produces new and interesting results about the axial and azimuthal modes not previously published in the literature. In particular, when a liquid layer coats the outside of a cylinder it was found that the azimuthal mode, n=1, is the most important in a range of the nondimensional surface tension where the purely axial mode dominated in the absence of the inner cylinder. Additionally, it was found that some azimuthal spiral modes with a finite wavenumber appear as the most unstable in the presence of the inner cylinder. It was shown that the larger the centrifugal force is, the larger the nondimensional radius of the inner cylinder should be to make the instability more sensitive to the presence of the inner cylinder. An equation for the growth rate was obtained in the limit of very thin liquid layers and it was found that the maxima of growth rate agree very well with the experimental results of a fluid layer coating the outside of a rotating cylinder.