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- W28422498 abstract "This chapter discusses the stability of flow between rotating cylinders to periodic disturbances and the subsequent growth and equilibration of such disturbances for speeds above critical. The stability of a viscous flow between concentric rotating cylinders is one of the classical problems in the theory of hydrodynamic stability. An analysis of the stability of Couette flow based on the linearized equations for small disturbances leads to an eigenvalue problem for the critical speed of the inner cylinder in the form of a dimensionless combination T, the Taylor number. It is a function of the parameters μ = Ω2 /Ω1 and η = R1/R2 that describe the basic velocity and the geometry, and the dimensionless wave numbers describing the disturbance. Ω2 , Ω1 and R1, R2 are the angular velocities and radii of the inner and outer cylinders, respectively. This chapter discusses the values of η and μ for which one can expect the critical speed to correspond to an axisymmetric disturbance and the resulting motion for T > Tc , where Tc the critical value of T, to be the axisymmetric Taylor vortex motion. The chapter presents the development of the finite-amplitude Taylor vortex motion for T > Tc ." @default.
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- W28422498 date "1967-01-01" @default.
- W28422498 modified "2023-10-16" @default.
- W28422498 title "Vector Eigenfunction Expansions for the Growth of Taylor Vortices in the Flow between Rotating Cylinders" @default.
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- W28422498 doi "https://doi.org/10.1016/b978-1-4831-9647-3.50008-x" @default.
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