Ekman vortices and the centrifugal instability in counter-rotating cylindrical Couette flow

Theoretical and Computational Fluid Dynamics

Volumn 18, Issue 2-4, 2004, Pages 151-168

  Czarny, Olivier ^a   Serre, Eric ^a   Bontoux, Patrick ^a   Lueptow, Richard M ^b  

^a AIX MARSEILLE UNIVERSITÉ   (France)

^b Northwestern University   (United States)

Author keywords

Direct numerical simulation; Ekman; Taylor Couette

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY LAYERS; CAVITATION; COMPUTER SIMULATION; CYLINDERS (SHAPES); VISCOSITY; VORTEX FLOW;

DIRECT NUMERICAL SIMULATION; EKMAN VORTICES; TAYLOR-COUETTE FLOW; VISCOUS EFFECTS;

ROTATIONAL FLOW;

CENTRIFUGAL IMPELLER; COMPUTATIONAL FLUID DYNAMICS; COUETTE FLOW; INSTABILITY; MATHEMATICAL ANALYSIS; VORTICITY;

EID: 10644223527     PISSN: 09354964     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00162-004-0140-6     Document Type: Article

References (44)

1. Ahlers, G., Cannell, D.S.: Vortex-front propagation in rotating Couette-Taylor flow. Phys. Rev. Lett. 50, 1583-1586 (1983)
2. Alziary de Roquefort, T., Grillaud, G.: Computation of Taylor vortex flow by a transient implicit method. Computers Fluids 6, 259-269 (1978)
3. Andereck, C.D., Liu, S.S., Swinney, H.L.: Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155-183 (1986)
4. Antonijoan, J., Marques, F., Sanchez, J.: Non-linear spirals in the Taylor-Couette Problem. Phys. Fluids 10, 829-838 (1998)
5. Antonijoan, J., Sanchez, J.: Transitions from Taylor vortex flow in a co-rotating Taylor-Couette system. Phys. Fluids 12, 3147-3159 (2000)
6. Benjamin, T.B.: Bifurcation phenomena in steady flows of a viscous fluid I: Theory. Proc. R. Soc. Lond. A 359, 1-26 (1978a)
7. Benjamin, T.B.: Bifurcation phenomena in steady flows of a viscous fluid II: Experiments. Proc. R. Soc. Lond. A 359, 27-43 (1978b)
8. Benjamin, T.B., Mullin, T.: Anomalous modes in the Taylor experiment. Proc. Roy. Soc. Lond. A 377, 221-249 (1981)
9. Burkhalter, J.E., Koschmieder, E.L.: Steady supercritical Taylor vortex flow. J. Fluid Mech. 58, 547-560 (1973)
10. Chossat, P., Iooss, G.: The Couette-Taylor Problem. NY, Springer-Verlag (1994)
11. Cliffe, K.A., Mullin, T.: A numerical and experimental study of anomalous modes in the Taylor experiment. J. Fluid Mech. 153, 243-258 (1985)
12. Cole, J.A.: Taylor-vortex instability and annulus-length effects. J. Fluid Mech. 75, 1-15 (1976)
13. Coles, D.: Transition in circular Couette flow. J. Fluid Mech. 21, 385-425 (1965)
14. Colovas, P.W., Andereck, C.D.: Turbulent bursting and spatiotemporal intermittency in the counter-rotating Taylor-Couette system. Phys. Rev. E 55, 2736-2741 (1997)
15. Czarny, O., Serre, E., Bontoux, P., Lueptow, R.M.: Identification of complex flows in Taylor-Couette counter-rotating cavities. C. R. Acad. Sci. Paris, Serie IIb 329, 1-7 (2001)
16. Czarny, O., Serre, E., Bontoux, P., Lueptow. R.M.: Spiral and wavy vortex flows in short counter-rotating Taylor-Couette cells. Theoret. Comput. Fluid Dynamics, 16, 5-15 (2002)
17. Czarny, O., Serre, E., Bontoux, P., Lueptow, R.M.: Interaction between Ekman pumping and the centrifugal instability in Taylor-Couette flow. Phys. Fluids 15, 467-477 (2003)
18. Czarny, O., Serre, E., Bontoux, P., Lueptow, R.M.: Interaction of wavy cylindrical Couette flow with endwalls. Phys. Fluids 16, 1140-1148 (2004)
19. Edwards, W.S., Tagg, R.P., Dornblaser, B.C., Swinney, H.L.: Periodic traveling waves with nonperiodic pressure. Eur. J. Mech., B/Fluids 10, 205-210 (1991)
20. Goharzadeh, A., Mutabazi, I.: Experimental characterization of intermittency regimes in the Couette-Taylor system. Eur. Phys. J. B 19, 157-162 (2001)
21. Golubitsky, M., Langford, W.F.: Pattern formation and bistability in flow between counterrotating cylinders. Physica D 32, 362-392 (1988)
22. Greenspan, H.P.: The Theory of Rotating Fluids. London, Camb. Uni. Press (1969)
23. Hegseth, J.J.. Andereck, C.D., Hayot. F., Pomeau, Y.: Spiral turbulence and phase dynamics. Phys. Rev. Lett. 62, 257-260 (1989)
24. Hegseth, J.J., Baxter, G.W., Andereck, C.D.: Bifurcations from Taylor vortices between corotating concentric cylinders. Phys. Rev. E 53, 507-521 (1996)
25. Jones, CA.: On flow between counter-rotating cylinders. J. Fluid Mech., 120, 433-450 (1982)
26. Jones, C.A.: The transition to wavy Taylor vortices. J. Fluid Mech. 157, 135-162 (1985)
27. King, G.P., Li, Y., Lee, W., Swinney, H.L, Marcus. P.S.: Wave speeds in wavy Taylor-vortex flow. J. Fluid Mech. 141, 365-390 (1984)
28. Kuo, D.-C., Ball, K.S.: Taylor-Couette flow with buoyancy: Onset of spiral flow. Phys. Fluids 9. 2872-2884 (1997)
29. Lingwood, R.J.: Absolute instability of the Ekman layer and related rotating flows. J. Fluid Meeh. 331, 405-428 (1997)
30. Lorenzen, A., Mullin, T.: Anomalous modes and finite-length effects in Taylor-Couette flow. Physical Review A 31, 3463-3465 (1985)
31. Lorenzen, A., Pfister, G., Mullin, T: End effects on the transition to time-dependent motion in the Taylor experiment. Phys. Fluids 26, 10-13 (1983)
32. Lücke, M., Mihelcic, M., Wingerath, K.: Front propagation and pattern formation of Taylor vortices growing into unstable circular Couette flow. Phys. Rev. A 31, 396-409 (1985)
33. Meincke, O., Egbers, C.: Routes to chaos in small and wide gap Taylor-Couette flow. Phys. Chem. Earth (B) 24, 467-471 (1999)
34. Mullin, T.: Finite-dimensional dynamics in Taylor-Couette flow. IMA J. Appl. Math., 46, 109-119 (1991)
35. Pfister, G., Rehberg, I.: Space-dependent order parameter in circular Couette flow transitions. Phys. Lett. 83A, 19-22 (1981)
36. Raspo, I., Hughes, S., Serre, E., Randriamampianina, A., Bontoux, P.: Spectral projection methods for the simulation of complex three-dimensional rotating flows. Computers Fluids 31, 745-767 (2001)
37. Sanchez, J., Crespo, D., Marques, R.: Spiral vortices between concentric cylinders. Appl. Sci. Res. 51, 55-59 (1993)
38. Serre, E., Crespo del Arco, E., Bontoux, P.: Annular and spiral patterns in flows between rotating and stationary discs. J. Fluid Mech. 434, 65-100 (2001)
39. Snyder, H.A.: Waveforms in rotating Couette flow. Int. J. Non-Linear Mech. 5, 659-685 (1970)
40. Sobolik, V., Izrar, B., Lusseyran, R., Skali, S.: Interaction between the Ekman layer and the Couette-Taylor instability. Int. J. Heat Mass Trans. 43, 4381-4393 (2000)
41. Stern, C., Hussain, F.: Chaos in counter-rotating Couette flow. Physica D 72, 195-210 (1994)
42. Van Atta, C.: Exploratory measurements in spiral turbulence. J. Fluid Mech. 25, 495-512 (1966)
43. Vanel, J.M., Peyret, R., Bontoux, P.: A pseudospectral solution of vorticity streamfunction equations using the influence matrix technique. In Numerical Methods for Fluid Dynamics II. Edited by Morton, K.W., Baines, M.J., pp. 463-475 (1986)
44. Weisshaar, E., Busse, F.H., Nagata, M.: Twist vortices and their instabilities in the Taylor-Couette system. J. Fluid Mech. 226, 549-564 (1991)