On the linear stability of spiral flow between rotating cylinders

A numerical study is carried out of the effects of both axisymmetric and nonaxisymmetric disturbances on the stability of spiral flow between rotating cylinders. The main difference between the study described here and previous investigations is that, by using the compound matrix method, it is possible to extend the stability calculations to much higher Reynolds numbers than has hitherto been possible. It is noted that although only the case of a fixed outer cylinder for which mu = 0 (mu being the ratio of the angular speed of the outer cylinder to that of the inner cylinder) is studied, the numerical scheme developed here can be applied to other rotational speed ratios. For axisymmetric disturbances, the calculations for eta = 0.95 (eta being the ratio of the radius of the inner cylinder to that of the outer cylinder) lead to the discovery of a new 'rotational' mode of instability with wavenumbers and wave speed substantially different from those of the usual Tollmien-Schlichting mode associated with viscous effects.