Mode competition of rotating waves in reflection-symmetric Taylor-Couette flow

Journal of Fluid Mechanics

Volumn 540, Issue , 2005, Pages 269-299

  Abshagen, J ^a   Lopez, J M ^b   Marques, F ^c   Pfister, G ^a  

^a UNIVERSITY OF KIEL   (Germany)

^b ARIZONA STATE UNIVERSITY   (United States)

^c UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); FLOW INTERACTIONS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; VORTEX FLOW;

HOPF BIFURCATION; ROTATING WAVES; TAYLOR-COUETTE FLOW;

ROTATIONAL FLOW;

BIFURCATION; FLUID MECHANICS; ROTATING FLOW; TAYLOR-COUETTE FLOW; VORTEX FLOW;

EID: 26944486562     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112005005811     Document Type: Article

References (41)

1. Abshagen, J., Lopez, J. M., Marques, F. & Pfister, G. 2005 Symmetry breaking via global bifurcations of modulated rotating waves in hydrodynamics. Phys. Rev. Lett. 94, 074101.
2. Abshagen, J., Pfister, G. & Mullin, T. 2001 Gluing bifurcations in a dynamically complicated extended flow. Phys. Rev. Lett. 87, 224501.
3. Benjamin, T. B. 1978a Bifurcation phenomena in steady flows of a viscous fluid. Proc. R. Soc. Lond. A 359, 1-26.
4. Benjamin, T. B. 1978b Bifurcation phenomena in steady flows of a viscous fluid. II. Experiments. Proc. R. Soc. Lond. A 359, 27-43.
5. Benjamin, T. B. & Mullin, T. 1982 Notes on the multiplicity of flows in the Taylor experiment. J. Fluid Mech. 121, 219-230.
6. Blackburn, H. M. & Lopez, J. M. 2002 Modulated rotating waves in an enclosed swirling flow. J. Fluid Mech. 465, 33-58.
7. Chossat, P. & Iooss, G. 1994 The Couette-Taylor Problem. Springer.
8. Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385-425.
9. Crawford, J. D. & Knobloch E. 1991 Symmetry and symmetry-breaking bifurcations in fluid dynamics. Annu. Rev. Fluid Mech. 23, 341-387.
10. DiPrima, R. C. & Swinney, H. L. 1981 Instabilities and transition in flow between concentric rotating cylinders. In Hydrodynamics Instabilities and the Transtion to Turbulence (ed. H. L. Swinney & J. P. Gollub). Topics in Applied Physics, vol. 45. Springer.
11. Egbers, C. & Pfister, G. (Eds.) 2000 Physics of Rotating Fluids. Lecture Notes in Physics, vol. 549. Springer.
12. Gerdts, U., Von Stamm, J., Buzug, T. & Pfister, G. 1994 Axisymmetric time-dependent flow in the Taylor-Couette system. Phys. Rev. E 49, 4019-4026.
13. Guckenheimer, J. & Holmes, P. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.
14. Iooss, G. & Adelmeyer, M. 1998 Topics in Bifurcation Theory and Applications, 2nd edn. World Scientific.
15. Kevrekidis, I. G., Rico-Martínez, R., Ecke, R. E., Farber, R. M. & Lapedes, A. S. 1994 Global bifurcations in Raleigh-Bénard convection. Experiments, empirical maps and numerical bifurcation analysis. Physica D 71, 342-362.
16. 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.
17. Krupa, M. 1990 Bifurcations of relative equilibria. SIAM J. Math. Anal. 21, 1453-1486.
18. Kuznetsov, Y. A. 1998 Elements of Applied Bifurcation Theory, 2nd edn. Springer.
19. Lopez, J. M., Hart, J. E., Marques, F., Kittelman, S. & Shen, J. 2002 a Instability and mode interactions in a differentially-driven rotating cylinder. J. Fluid Mech. 462, 383-409.
20. Lopez, J. M. & Marques, F. 2003 Small aspect ratio Taylor-Couette flow: Onset of a very-low-frequency three-torus state. Phys. Rev. E 68, 036302.
21. Lopez, J. M. & Marques, F. 2004 Mode competition between rotating waves in a swirling flow with reflection symmetry. J. Fluid Mech. 507 265-288.
22. Lopez, J. M., Marques, F. & Fernando, H. J. S. (Eds.) 2004a Theoret. Comput. Fluid Dyn.; special issue Taylor-Couette Flows, vol. 18(2-4). Springer.
23. 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.
24. Lopez, J. M., Marques, F. & Shen, J. 2004b Complex dynamics in a short Taylor-Couette annulus with the top endwall stationary and the bottom rotating. J. Fluid Mech. 501, 327-354.
25. 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.
26. 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.
27. Mullin, T. 1982 Mutations of steady cellular flows in the Taylor experiments. J. Fluid Mech. 121, 207-218.
28. Mullin, T. 1991 Finite-dimensional dynamics in Taylor-Couette flow. IMA J. Appl. Maths 46, 109-119.
29. Mullin, T. 1993 The Nature of Chaos. Oxford University Press.
30. Mullin, T. & Blohm, C. 2001 Bifurcation phenomena in a Taylor-Couette flow with asymmetric boundary conditions. Phys. Fluids 13, 136-140.
31. Mullin, T., Tavener, S. J. & Cliffe, K. A. 1989 An experimental and numerical study of a codimension-2 bifurcation in a rotating annulus. Europhys. Lett. 8, 251-256.
32. Mullin, T., Toya, Y. & Tavener, S. J. 2002 Symmetry breaking and multiplicity of states in small aspect ratio Taylor-Couette flow. Phys. Fluids 14, 2778-2787.
33. Nore, C., Tuckerman, L. S., Daube, O. & Xin, S. 2003 The 1:2 mode interaction in exactly counter-rotating von Karman swirling. J. Fluid Mech. 477, 51-88.
34. Peacock, T. & Mullin, T. 2001 Homoclinic bifurcations in a liquid crystal flow. J. Fluid Mech. 432, 369-386.
35. Price, T. J. & Mullin, T. 1991 An experimental observation of a new type of intermittency. Physica D 48, 29-52.
36. von Stamm, J., Gerdts, U., Buzug, T. & Pfister, G. 1996 Symmetry breaking and period doubling on a torus in the VLF regime in Taylor-Couette flow. Phys. Rev. E 54, 4938-4957.
37. Strogatz, S. 1994 Nonlinear Dynamics and Chaos. Addison-Wesley.
38. Swift, J. W. & Wiesenfeld, K. 1984 Suppression of period doubling in symmetric systems. Phys. Rev. Lett. 52, 705-708.
39. Tagg, R. P. 1994 The Couette-Taylor problem. Nonlinear Sci. Today 4, 1-25.
40. Tuckerman, L. S. & Barkley, D. 1988 Global bifurcation to traveling waves in axisymmetric convection. Phys. Rev. Lett. 61, 408-411.
41. Wiggins, S. 1988 Global Bifurcations and Chaos. Springer.