Rotating and modulated rotating waves in transitions of an enclosed swirling flow

Journal of Fluid Mechanics

Volumn 553, Issue , 2006, Pages 323-346

  Lopez, J M ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; BIFURCATION (MATHEMATICS); CYLINDERS (SHAPES); REYNOLDS NUMBER; ROTATION; SPATIAL VARIABLES MEASUREMENT; TRANSITION FLOW;

APERIODIC FLOW; AXISYMMETRIC FLOW; ROTATING WAVES; SPATIO-TEMPORAL SYMMETRIES;

SWIRLING FLOW;

ASPECT RATIO; BIFURCATION (MATHEMATICS); CYLINDERS (SHAPES); REYNOLDS NUMBER; ROTATION; SPATIAL VARIABLES MEASUREMENT; SWIRLING FLOW; TRANSITION FLOW;

FLUID MECHANICS;

EID: 33645653847     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112006008962     Document Type: Article

References (61)

1. Barkley, D. & Henderson, R. D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215-241.
2. Bayliss, A., Matkowsky, B. J. & Riecke, H. 1994 Structure and dynamics of modulated traveling waves in cellular flames. Physica D 74, 1-23.
3. Blackburn, H. M. & Lopez, J. M. 2000 Symmetry breaking of the flow in a cylinder driven by a rotating end wall. Phys. Fluids 12, 2698-2701.
4. Blackburn, H. M. & Lopez, J. M. 2002 Modulated rotating waves in an enclosed swirling flow. J. Fluid Mech. 465, 33-58.
5. Blackburn, H. M., Marques, F. & Lopez, J. M. 2005 Symmetry breaking of two-dimensional time-periodic flows. J. Fluid Mech. 522, 395-411.
6. Brons, M., Voigt, L. K. & Sorensen, J. N. 1999 Streamline topology of steady axisymmetric vortex breakdown in a cylinder with co- and counter-rotating end-covers. J. Fluid Mech. 401, 275-292.
7. Chossat, P. & Iooss, G. 1994 The Couette-Taylor Problem. Springer.
8. Chossat, P. & Lauterbach, R. 2000 Methods in Equivariant Bifurcations and Dynamical Systems. World Scientific.
9. Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385-425.
10. Crawford, J. D. & Knobloch, E. 1991 Symmetry and symmetry-breaking bifurcations in fluid dynamics. Annu. Rev. Fluid Mech. 23, 341-387.
11. Escudier, M. P. 1984 Observations of the flow produced in a cylindrical container by a rotating endwall. Exps. Fluids 2, 189-196.
12. Feigenbaum, M. J. 1978 Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 19, 25.
13. Gauthier, G., Gondret, P., Moisy, F. & Rabaud, M. 2002 Instabilities in the flow between co- and counter-rotating disks. J. Fluid Mech. 473, 1-21.
14. Gauthier, G., Gondret, P. & Rabaud, M. 1999 Axisymmetric propagating vortices in the flow between a stationary and a rotating disk enclosed by a cylinder. J. Fluid Mech. 386, 105-126.
15. Gelfgat, A. Y., Bar-Yoseph, P. Z. & Solan, A. 1996 Stability of confined swirling flow with and without vortex breakdown. J. Fluid Mech. 311, 1-36.
16. Gelfgat, A. Y., Bar-Yoseph, P. Z. & Solan, A. 2001 Three-dimensional instability of axisymmetric flow in a rotating lid-cylinder enclosure. J. Fluid Mech. 438, 363-377.
17. Golubitsky, M., LeBlanc, V. G. & Melbourne, I. 2000 Hopf bifurcation from rotating waves and patterns in physical space. J. Nonlinear Sci. 10, 69-101.
18. Golubitsky, M. & Stewart, I. 2002 The Symmetry Perspective: From Equilbrium to Chaos in Phase Space and Physical Space. Birkhäuser.
19. Switzer, G. & Proctor, F. 2000 Numerical study of wake vortex behavior in turbulent domains with ambient stratification. 38th Aerospace Sciences Meeting & Exhibit, Reno, NV, AIAA 2000-0755.
20. Gorman, M., el Hamdi, M., Pearson, B. & Robbins, K. A. 1996 Ratcheting motion of concentric rings in cellular flames. Phys. Rev. Lett. 76, 228-231.
21. Gorman, M., Hamill, C. F., el Hamdi, M. & Robbins, K. A. 1994 Rotating and modulated rotating states of cellular flames. Combust. Sci. Technol. 98, 25-35.
22. Gorman, M. & Swinney, H. L. 1982 Spatial and temporal characteristics of modulated waves in the circular Couette system. J. Fluid Mech. 117, 123-142.
23. Gorman, M., Swinney, H. L. & Rand, D. A. 1982 Doubly periodic circular Couette flow: Experiments compared with predictions from dynamics and symmetry. Phys. Rev. Lett. 46, 992-995.
24. Guckenheimer, J. & Holmes, P. 1997 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.
25. Hide, R. & Titman, C. W. 1967 Detached shear layers in a rotating fluid. J. Fluid Mech. 29, 39-60.
26. Iooss, G. & Adelmeyer, M. 1998 Topics in Bifurcation Theory and Applications, 2nd edn. World Scientific.
27. Knobloch, E. 1994 Bifurcations in rotating systems. In Lectures on Solar and Planetary Dynamos (ed. M. R. E. Proctor & A. D. Gilbert), pp. 331-372. Cambridge University Press.
28. Knobloch, E. 1996 Symmetry and instability in rotating hydrodynamic and magnetohydrodynamic flows. Phys. Fluids 8, 1446-1454.
29. Krupa, M. 1990 Bifurcations of relative equilibria. SIAM J. Math. Anal. 21, 1453-1486.
30. Kuznetsov, Y. A. 1998 Elements of Applied Bifurcation Theory, 2nd edn. Springer.
31. Lopez, J. M. 1990 Axisymmetric vortex breakdown. Part 1. Confined swirling flow. J. Fluid Mech. 221, 533-552.
32. Lopez, J. M. 1998 Characteristics of endwall and sidewall boundary layers in a rotating cylinder with a differentially rotating endwall. J. Fluid Mech. 359, 49-79.
33. Lopez, J. M., Hart, J. E., Marques, F., Kittelman, S. & Shen, J. 2002a Instability and mode interactions in a differentially-driven rotating cylinder. J. Fluid Mech. 462, 383-409.
34. Lopez, J. M. & Marques, F. 2004 Mode competition between rotating waves in a swirling flow with reflection symmetry. J. Fluid Mech. 507, 265-288.
35. Lopez, J. M., Marques, F. & Sanchez, J. 2001 Oscillatory modes in an enclosed swirling flow. J. Fluid Mech. 439, 109-129.
36. Lopez, J. M., Marques, F. & Shen, J. 2002b An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries II. Three dimensional cases. J. Comput. Phys. 176, 384-401.
37. Lopez, J. M. & Perry, A. D. 1992 Axisymmetric vortex breakdown. Part 3. Onset of periodic flow and chaotic advection. J. Fluid Mech. 234, 449-471.
38. Lopez, J. M. & Shen, J. 1998 An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries I. Axisymmetric cases. J. Comput. Phys. 139, 308-326.
39. Lugt, H. J. & Abboud, M. 1987 Axisymmetric vortex breakdown with and without temperature effects in a container with a rotating lid. J. Fluid Mech. 179, 179-200.
40. Marques, F. & Lopez, J. M. 2001 Precessing vortex breakdown mode in an enclosed cylinder flow. Phys. Fluids 13, 1679-1682.
41. 2 spatio-temporal and O(2) spatial symmetry. Physica D 189, 247-276.
42. Marques, F., Lopez, J. M. & Shen, J. 2002 Mode interactions in an enclosed swirling flow: A double Hopf bifurcation between azimuthal wavenumbers 0 and 2. J. Fluid Mech. 455, 263-281.
43. Moisy, F., Pasutto, T. & Rabaud, M. 2003 Instability patterns between counter-rotating disks. Nonlinear Process. Geophys. 10, 281-288.
44. Mullin, T. 1999 Flow state multiplicity in convection. Phys. Fluids 11, 2815-2817.
45. m, m ≥ 3. Commun. Math. Phys. 64, 35.
46. Nore, C., Moisy, F. & Quartier, L. 2005 Experimental observation of near-heteroclinic cycles in the von Kármán swirling flow. Phys. Fluids 17, 064103.
47. Nore, C., Tuckerman, L. S., Daube, O. & Xin, S. 2003 The 1:2 mode interaction in exactly counter-rotating von Kármán swirling flow. J. Fluid Mech. 477, 51-88.
48. Rand, D. 1982 Dynamics and symmetry. Predictions for modulated waves in rotating fluids. Arch. Rat. Mech. Anal. 79, 1-38.
49. Read, P. L. 2001 Transition to geostrophic turbulence in the laboratory, and as a paradigm in atmospheres and oceans. Surv. in Geophys. 22, 265-317.
50. Renardy, M. 1982 Bifurcation from rotating waves. Arch. Rat. Mech. Anal. 79, 49-84.
51. Ruelle, D. & Takens, F. 1971 On the nature of turbulence. Commun. Math. Phys. 20, 167.
52. Schouveiler, L., Gal, P. L., Chauve, M. P. & Takeda, Y. 1999 Spiral and circular waves in the flow between a rotating and a stationary disc. Exps. Fluids 26, 179-187.
53. Serre, E. & Bontoux, P. 2002 Vortex breakdown in a three-dimensional swirling flow. J. Fluid Mech. 459, 347-370.
54. Serre, E., Tuliszka-Sznitko, E. & Bontoux, P. 2004 Coupled numerical and theoretical study of the flow transition between a rotating and a stationary disk. Phys. Fluids 16, 688-706.
55. Sorensen, J. N. & Christensen, E. A. 1995 Direct numerical simulation of rotating fluid flow in a closed cylinder. Phys. Fluids 7, 764-778.
56. Sotiropoulos, F. & Ventikos, Y. 2001 The three-dimensional structure of confined swirling flows with vortex breakdown. J. Fluid Mech. 426, 155-175.
57. Sotiropoulos, F., Ventikos, Y. & Lackey, T. C. 2001 Chaotic advection in a three-dimensional stationary vortex-breakdown bubbles: Šil'nikov's chaos and the devil's staircase. J. Fluid Mech. 444, 257-297.
58. Spohn, A., Mory, M. & Hopfinger, E. J. 1998 Experiments on vortex breakdown in a confined flow generated by a rotating disk. J. Fluid Mech. 370, 73-99.
59. Stevens, J. L., Lopez, J. M. & Cantwell, B. J. 1999 Oscillatory flow states in an enclosed cylinder with a rotating endwall. J. Fluid Mech. 389, 101-118.
60. Swift, J. W. & Wiesenfeld, K. 1984 Suppression of period doubling in symmetric systems. Phys. Rev. Lett. 52, 705-708.
61. Ventikos, Y. 2002 The effect of imperfections on the emergence of three-dimensionality in stationary vortex breakdown bubbles. Phys. Fluids 14, 13-16.