Applied Mechanics pp 1037-1044 | Cite as

Nonlinear aspects of instability in flow between rotating cylinders

  • R. C. DiPrima
  • J. T. Stuart
Conference paper


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 = Ω21 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 Ω12 and R 1/R 2 are the angular velocities and radii of the inner and outer cylinders respectively.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1966

Authors and Affiliations

  • R. C. DiPrima
    • 1
  • J. T. Stuart
    • 2
  1. 1.Rensselaer Polytechnic InstituteTroyUSA
  2. 2.National Physical LaboratoryTeddingtonUK

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