Nonlinear aspects of instability in flow between rotating cylinders
Since Taylor’s (1923) original investigation of the stability of a viscous flow between concentric rotating cylinders, this particular flow has received considerable attention. Taylor observed that, at sufficiently high speeds of the inner cylinder, the laminar circumferential flow (Couette flow) becomes unstable, the instability yielding a steady secondary motion in the form of toroidal vortices (Taylor vortices) spaced regularly along the axis of the cylinders. The linearized problem for the stability of the flow with respect to axisymmetric disturbances leads to an eigenvalue problem for the critical speed of the inner cylinder, which appears in the form of a Taylor number T. It is a function of the parameters μ = Ω2/Ω1 and η = R 1/R 2 which describe the basic velocity and the geometry up to scale factors, and the dimensionless wave number X of the disturbance. Here Ω1/Ω2 and R 1/R 2 are the angular velocities and radii of the inner and outer cylinders respectively.
Unable to display preview. Download preview PDF.
- Bisshopp, F.: Flow Between Concentric Rotating Cylinders — A Note on the Narrow Gap Approximation. Technical Report 51, ONR Contract Nonr 562(07), Brown University, 1963.Google Scholar
- Coles, D.: Paper presented at the Tenth International Congress of Applied Mechanics, Stresa, Italy, 1960 (see Proceedings of that Congress, Amsterdam: Elsevier 1962, p. 163).Google Scholar
- Coles, D.: Interfaces and Intermittency in Turbulent Shear Flows, see “Mécanique de la Turbulence” (Proceedings of Marseilles meeting 1961), Centre National de la Recherche Scientifique, Paris 1962, pp. 229-250.Google Scholar
- Krueger, E. R.: The Stability of Couette Flow and Spiral Flow. Ph. D. Thesis, Rensselaer Polytechnic Institute, Troy, N. Y. 1962.Google Scholar
- Krueger, E. R., A. Gross and R. C. DiPrima: J. Fluid Mech. 1966 (to be published).Google Scholar
- Schultz-Grunow, F., and H. Hein: Beitrag zur Couetteströmung. Z. Flugwiss. 4 (1956) 28–30.Google Scholar
- Stuart, J. T.: On Three-Dimensional Non-Linear Effects in the Stability of Parallel Flows. Advances in Aeronautical Sciences, Vols. 3-4, Pergamon Press 1961, pp. 121-142.Google Scholar
- Stuart, J. T.: Contribution to “Stability of Systems”, Discussion at I. Mech. E. London, May 21/22, 1964. I. Mech. E. Proc. 178, Pt.3M, 1965.Google Scholar