Time scales for transition in Taylor-Couette flow

Physics of Fluids

Volumn 19, Issue 5, 2007, Pages

  Czarny, Olivier ^a,b   Lueptow, Richard M ^c  

^a IRFM   (France)

^b AIX MARSEILLE UNIVERSITY   (France)

^c NORTHWESTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIRECT NUMERICAL SIMULATION; LINEAR STABILITY ANALYSIS; VISCOUS FLOW; VORTEX FLOW; WALL FLOW;

SUPERCRITICAL-TO-SUBCRITICAL TRANSITION; TAYLOR-COUETTE FLOW;

TRANSITION FLOW;

DIRECT NUMERICAL SIMULATION; LINEAR STABILITY ANALYSIS; TRANSITION FLOW; VISCOUS FLOW; VORTEX FLOW; WALL FLOW;

EID: 34249977620     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2728785     Document Type: Article

References (39)

1. G.Pfister and I. Rehberg, "Space-dependent order parameter in circular Couette flow transitions," Phys. Lett. PYLAAG0375-960110.1016/0375-9601(81)90537-5 83A, 19 (1981).
2. G. Ahlers and D. S. Cannell, "Vortex-front propagation in rotating Couette-Taylor flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.50.1583 50, 1583 (1983).
3. M. Lücke, M. Mihelcic, and K. Wingerath, "Front propagation and pattern formation of Taylor vortices growing into unstable circular Couette flow," Phys. Rev. A PLRAAN1050-294710.1103/PhysRevA.31.396 31, 396 (1985).
4. O. Czarny, E. Serre, P. Bontoux, and R. M. Lueptow, "Interaction between Ekman pumping and the centrifugal instability in Taylor-Couette flow," Phys. Fluids PHFLE61070-663110.1063/1.1534108 15, 467 (2003).
5. T. B. Benjamin, "Bifurcation phenomena in steady flows of a viscous fluid. I: Theory," Proc. R. Soc. London, Ser. A PRLAAZ1364-5021 359, 1 (1978).
6. T. Alziary de Roquefort and G. Grillaud, "Computation of Taylor vortex flow by a transient implicit method," Comput. Fluids CPFLBI0045-793010.1016/0045-7930(78)90017-8 6, 259 (1978).
7. D.-C. Kuo and K. S. Ball, "Taylor-Couette flow with buoyancy: Onset of spiral flow," Phys. Fluids PHFLE61070-663110.1063/1.869400 9, 2872 (1997).
8. V. Sobolik, B. Izrar, R. Lusseyran, and S. Skali, "Interaction between the Ekman layer and the Couette-Taylor instability," Int. J. Heat Mass Transfer IJHMAK0017-931010.1016/S0017-9310(00)00067-3 43, 4381 (2000).
9. J. Abshagen, O. Meincke, G. Pfister, K. A. Cliffe, and T. Mullin, "Transient dynamics at the onset of Taylor vortices," J. Fluid Mech. JFLSA70022-112010.1017/S002211200200321X 476, 335 (2003).
10. J. E. Burkhalter and E. L. Koschmieder, "Steady supercritical Taylor vortex flow," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112073002326 58, 547 (1973).
11. T. B. Benjamin, "Bifurcation phenomena in steady flows of a viscous fluid. II: Experiments," Proc. R. Soc. London, Ser. A PRLAAZ1364-5021 359, 27 (1978).
12. T. B. Benjamin and T. Mullin, "Anomalous modes in the Taylor experiment," Proc. R. Soc. London, Ser. A PRLAAZ1364-5021 377, 221 (1981).
13. K. A. Cliffe and T. Mullin, "A numerical and experimental study of anomalous modes in the Taylor experiment," J. Fluid Mech. JFLSA70022-112010.1017/S0022112085001240 153, 243 (1985).
14. A. Lorenzen and T. Mullin, "Anomalous modes and finite-length effects in Taylor-Couette flow," Phys. Rev. A PLRAAN1050-294710.1103/PhysRevA.31.3463 31, 3463 (1985).
15. M. Niklas, M. Lücke, and H. Müller-Krumbhaar, "Velocity of a propagating Taylor-vortex front," Phys. Rev. A PLRAAN1050-294710.1103/PhysRevA.40.493 40, 493 (1989).
16. H. A. Snyder, "Wave-number selection at finite amplitude in rotating Couette flow," J. Fluid Mech. JFLSA70022-112010.1017/ S002211206900111X 35, 273 (1969).
17. K. Park, G. L. Crawford, and R. J. Donnelly, "Determination of transition in Couette flow in finite geometries," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.47.1448 47, 1448 (1981).
18. G. P. Neitzel, "Numerical computation of time-dependent Taylor-vortex flows in finite-length geometries," J. Fluid Mech. JFLSA70022-112010.1017/S0022112084000732 141, 51 (1984).
19. T. H. Squire, D. F. Jankowski, and G. P. Neitzel, "Experiments with deceleration from a Taylor-vortex flow," Phys. Fluids PFLDAS0031-917110.1063/1.865515 29, 2742 (1986).
20. J. K. Koga and E. L. Koschmieder, "Taylor vortices in short fluid columns," Phys. Fluids A PFADEB0899-821310.1063/1.857325 1, 1475 (1989).
21. R. J. Weiner, P. W. Hammer, C. E. Swanson, and R. J. Donnelly, "Stability of Taylor-Couette flow subject to an external Coriolis force," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.64.1115 64, 1115 (1990).
22. P. W. Hammer, R. J. Weiner, and R. J. Donnelly, "Bifurcation phenomena in nonaxisymmetric Taylor-Couette flow," Phys. Rev. A PLRAAN1050-294710.1103/PhysRevA.46.7578 46, 7578 (1992).
23. E. Ikeda and T. Maxworthy, "Spatially forced corotating Taylor-Couette flow," Phys. Rev. E PLEEE81063-651X10.1103/ PhysRevE.49.5218 49, 5218 (1994).
24. D. Hirshfeld and D. C. Rapaport, "Growth of Taylor vortices: A molecular dynamics study," Phys. Rev. E PLEEE81063-651X10.1103/ PhysRevE.61.R21 61, R21 (2000).
25. Q. Xiao, T. T. Lim, and Y. T. Chew, "Second Taylor vortex flow: Effects of radius ratio and aspect ratio," Phys. Fluids PHFLE61070-663110.1063/1.1452475 14, 1537 (2002).
26. B. Dubrulle, O. Dauchot, F. Daviaud, P.-Y. Longaretti, D. Richard, and J.-P. Zahn, "Stability and turbulent transport in Taylor-Couette flow from analysis of experimental data," Phys. Fluids PHFLE61070-663110.1063/1.2008999 17, 095103 (2005).
27. R. C. DiPrima and H. L. Swinney, in Topics in Applied Physics, Hydrodynamic Instabilities and the Transition to Turbulence, edited by H. L. Swinney and J. P. Gollub (Springer-Verlag, Berlin, 1985), pp. 139-180.
28. Y. Takeda, K. Kobashi, and W. E. Fischer, "Observation of the transient behaviour of Taylor vortex flow between rotating concentric cylinders after sudden start," Exp. Fluids EXFLDU0723-486410.1007/ BF00188759 9, 317 (1990).
29. K. Park, G. L. Crawford, and R. J. Donnelly, "Characteristic lengths in the wavy vortex state of Taylor-Couette flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.51.1352 51, 1352 (1983).
30. G. P. King and H. L. Swinney, "Limits of stability and irregular flow patterns in wavy vortex flow," Phys. Rev. A PLRAAN1050-294710.1103/PhysRevA.27.1240 27, 1240 (1983).
31. S. T. Wereley and R. M. Lueptow, "Azimuthal velocity in supercritical circular Couette flow," Exp. Fluids EXFLDU0723-486410.1007/BF00209355 18, 1 (1994).
32. H. P. Greenspan, The Theory of Rotating Fluids (Cambridge University Press, London, 1969).
33. P. Manneville, private Communication (2006). From numerical simulations, there are two stages to the onset transient based on the relaxation time of vortex wavelengths. The early stage of the onset transient is related to propagation of the front of the bifurcated state from the endwalls, while the late stage is related to slow wavelength adjustment related to phase diffusion for aspect ratios Iγ>16.
34. E. Serre, E. Crespo del Arco, and P. Bontoux, "Annular and spiral patterns in flows between rotating and stationary discs," J. Fluid Mech. JFLSA70022-112010.1017/S0022112001003494 434, 65 (2001).
35. O. Czarny, E. Serre, P. Bontoux, and R. M. Lueptow, "Interaction of wavy cylindrical Couette flow with the endwalls," Phys. Fluids PHFLE61070-663110.1063/1.1652671 16, 1140 (2004).
36. J. M. Vanel, R. Peyret, and P. Bontoux, in Numerical Methods for Fluid Dynamics II, edited by K. W. Morton and M. J. Baines (Clarendon, Oxford, 1986), pp. 463-475.
37. I. Raspo, S. Hughes, E. Serre, A. Randriamampianina, and P. Bontoux, "A spectral projection method for the simulation of complex three-dimensional rotating flows," Comput. Fluids CPFLBI0045-793010.1016/S0045-7930(01)00070-6 31, 745 (2002).
38. R. C. DiPrima, P. M. Eagles, and B. S. Ng, "The effect of radius ratio on the stability of Couette flow and Taylor vortex flow," Phys. Fluids PFLDAS0031-917110.1063/1.864544 27, 2403 (1984).
39. A. Recktenwald, M. Lücke, and H. W. Müller, "Taylor vortex formation in axial through-flow: Linear and weakly nonlinear analysis," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.48.4444 48, 4444 (1993).