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T. B. Benjamin, “Bifurcation Phenomena in Steady Flows of a Viscous Fluid I, Theory”, Proceedings of the Royal Society A, Vol. 79, No. 1696, 1978, pp. 1-26. doi:10.1098/rspa.1978.0028

has been cited by the following article:

• TITLE: Time Constants of the Transition between Onset and Decay Reynolds Numbers for the Appearance of Taylor-Couette Flow

  AUTHORS: Takashi Watanabe

  KEYWORDS: Taylor-Couette Flow; Onset/Decay Flow; Time Scale; Stuart-Landau Equation

  JOURNAL NAME: World Journal of Mechanics, Vol.2 No.2, April 26, 2012

  ABSTRACT: We investigate the onset and the decay of Taylor-Couette flow in finite cylinders, and we report the estimated time scales in the azimuthal section of the flow state transition between the super-critical state and the sub-critical state by fitting the numerical result to the solution of the Stuart-Landau equation. The inner cylinder rotates, and the outer cylinder and both end walls of the cylinders are stationary. Near the end walls of the cylinders, the value of the time scale is small. In the inner region, the radial velocity component has a large time scale near the center of the vortices, while the axial velocity component has a large time scale between the vortices.