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

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.

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.

Cite this paper

nullT. Watanabe, "Time Constants of the Transition between Onset and Decay Reynolds Numbers for the Appearance of Taylor-Couette Flow,"*World Journal of Mechanics*, Vol. 2 No. 2, 2012, pp. 77-83. doi: 10.4236/wjm.2012.22009.

nullT. Watanabe, "Time Constants of the Transition between Onset and Decay Reynolds Numbers for the Appearance of Taylor-Couette Flow,"

References

[1] R. Tagg, “The Taylor Couette Problem” Nonlinear Science Today, Vol. 4, 1994, pp. 1-25.

[2] 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

[3] T. B. Benjamin, “Bifurcation Phenomena in Steady Flows of a viscous Fluid II, Experiment”, Proceedings of the Royal Society A, Vol. 359, No. 1696, 1978, pp. 27-43. doi:10.1098/rspa.1978.0030

[4] T. Watanabe, H. Furukawa and I. Nakamura, “Nonlinear Development of Flow Patterns in an Annulus with decelerating Inner Cylinder”, Physics of Fluids, Vol. 14, No. 1, 2002, pp. 333-341.

[5] H. Furukawa, T. Watanabe, Y. Toya and I. Nakamura, “Flow Pattern Exchange in the Taylor-Couette System with a Very Small Aspect Ratio”, Physical Review E, Vol. 65, No. 3, 2002, Article ID: 036306. doi:10.1103/PhysRevE.65.036306

[6] E. L. Koschmieder, “Bénard Cells and Taylor Vortices”, Cambridge Univ. Press, Cambridge, 1993.

[7] J. Abshagen, O. Meincke, G. Pfister, K. A. Cliffe and T. Mullin, “Transient Dynamics at the Onset of Taylor Vortices”, Journal of Fluid Mechanics, Vol. 476, 2003, pp. 335-343. doi:10.1017/S002211200200321X

[8] P. Manneville and O. Czarny, “Aspect-Ratio Dependence of Transition Taylor Vortices Close to Threshold”, Theoretical and Computational Fluid Dynamics, Vol. 23, No. 1, 2009, pp. 15-36. doi:10.1007/s00162-009-0093-x

[1] R. Tagg, “The Taylor Couette Problem” Nonlinear Science Today, Vol. 4, 1994, pp. 1-25.

[2] 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

[3] T. B. Benjamin, “Bifurcation Phenomena in Steady Flows of a viscous Fluid II, Experiment”, Proceedings of the Royal Society A, Vol. 359, No. 1696, 1978, pp. 27-43. doi:10.1098/rspa.1978.0030

[4] T. Watanabe, H. Furukawa and I. Nakamura, “Nonlinear Development of Flow Patterns in an Annulus with decelerating Inner Cylinder”, Physics of Fluids, Vol. 14, No. 1, 2002, pp. 333-341.

[5] H. Furukawa, T. Watanabe, Y. Toya and I. Nakamura, “Flow Pattern Exchange in the Taylor-Couette System with a Very Small Aspect Ratio”, Physical Review E, Vol. 65, No. 3, 2002, Article ID: 036306. doi:10.1103/PhysRevE.65.036306

[6] E. L. Koschmieder, “Bénard Cells and Taylor Vortices”, Cambridge Univ. Press, Cambridge, 1993.

[7] J. Abshagen, O. Meincke, G. Pfister, K. A. Cliffe and T. Mullin, “Transient Dynamics at the Onset of Taylor Vortices”, Journal of Fluid Mechanics, Vol. 476, 2003, pp. 335-343. doi:10.1017/S002211200200321X

[8] P. Manneville and O. Czarny, “Aspect-Ratio Dependence of Transition Taylor Vortices Close to Threshold”, Theoretical and Computational Fluid Dynamics, Vol. 23, No. 1, 2009, pp. 15-36. doi:10.1007/s00162-009-0093-x