On the linear stability of spiral flow between rotating cylinders
Abstract
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 TollmienSchlichting mode associated with viscous effects.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 July 1982
 DOI:
 10.1098/rspa.1982.0091
 Bibcode:
 1982RSPSA.382...83N
 Keywords:

 Flow Stability;
 Reynolds Number;
 Rotating Cylinders;
 Viscous Flow;
 Vortices;
 Angular Velocity;
 Axisymmetric Flow;
 Flow Velocity;
 Fluid Mechanics and Heat Transfer