A periodically forced flow displaying symmetry breaking via a three-tori gluing bifurcation and two-tori resonances

Physica D: Nonlinear Phenomena

Volumn 156, Issue 1-2, 2001, Pages 81-97

  Marques, F ^a   Lopez, J M ^b   Shen, J ^c  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b ARIZONA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Gluing bifurcation; Naimark Sacker bifurcation; Periodic forcing; Symmetry breaking; Taylor Couette flow

Indexed keywords

EID: 0035427180     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(01)00261-5     Document Type: Article

References (33)

1. D. Ambruster B. Nicolaenko N. Smaoui P. Chossat Symmetries and dynamics for 2D Navier–Stokes flow Physica D 95 1996 81 93
2. V.S. Anishchenko M.A. Safonova L.O. Chua Confirmation of the Afraimovich–Shilnikov torus-breakdown theorem via a torus circuit IEEE Trans. Circuits Syst. I 40 1993 792 800
3. T.B. Benjamin Bifurcation phenomena in steady flows of a viscous fluid Proc. R. Soc. Lond. A 359 1978 1 26
4. T.B. Benjamin T. Mullin Anomalous modes in the Taylor experiment Proc. R. Soc. Lond. A 377 1981 221 249
5. H.M. Blackburn J.M. Lopez Symmetry breaking of the flow in a cylinder driven by a rotating endwall Phys. Fluids 12 2000 2698 2701
6. F.H. Busse, G. Pfister, D. Schwabe, Formation of dynamical structures in axisymmetric fluid systems, in: Evolution of Spontaneous Structures in Dissipative Continuous Systems, Lecture Notes in Physics, Vol. m55, Springer, Berlin, 1998, pp. 86–126.
7. A. Chenciner G. Iooss Bifurcation of invariant torus Arch. Rat. Mech. Anal. 69 1979 109 198
8. P. Chossat, G. Iooss, The Couette–Taylor Problem, Springer, Berlin, 1994.
9. K.A. Cliffe J.J. Kobine T. Mullin The role of anomalous modes in Taylor–Couette flow Phil. Trans. R. Soc. Lond. A 439 1992 341 357
10. K.A. Cliffe T. Mullin A numerical and experimental study of anomalous modes in the Taylor experiment J. Fluid Mech. 153 1985 243 258
11. 2, in: J.C. Martin, N.G. Markley, W. Perrizo (Eds.), The Structure of Attractors in Dynamical Systems, Springer Notes in Mathematics, Vol. 668, Springer, Berlin, 1978, pp. 48–66.
12. P. Gaspard Measurement of the instability rate of a far-from-equilibrium steady state at an infinite period bifurcation J. Phys. Chem. 94 1 1990 1 3
13. P. Glendinning Bifurcations near homoclinic orbits with symmetry Phys. Lett. A 103 1984 163 166
14. Y.A. Kuznetsov, Elements of Applied Bifurcation Theory, 2nd Edition, Springer, Berlin, 1998.
15. A.S. Landsberg E. Knobloch Oscillatory bifurcation with broken translation symmetry Phys. Rev. E 53 1996 3579 3600
16. J.M. Lopez F. Marques Dynamics of 3-tori in a periodically forced Navier–Stokes flow Phys. Rev. Lett. 85 2000 972 975
17. J.M. Lopez, F. Marques, J. Sanchez, Oscillatory modes in an enclosed swirling flow, J. Fluid Mech. (2001), in press.
18. J.M. Lopez F. Marques J. Shen Endwall effects in a periodically forced centrifugally unstable flow Fluid Dyn. Res. 27 2000 91 108
19. J.M. Lopez J. Shen An efficient spectral-projection method for the Navier–Stokes equations in cylindrical geometries. I. Axisymmetric cases J. Comput. Phys. 139 1998 308 326
20. F. Marques J.M. Lopez Taylor–Couette flow with axial oscillations of the inner cylinder: Floquet analysis of the basic flow J. Fluid Mech. 348 1997 153 175
21. F. Marques J.M. Lopez Spatial and temporal resonances in a periodically forced extended system Physica D 136 2000 340 352
22. T. Mullin Disordered fluid motion in a small closed system Physica D 62 1993 192 201
23. T. Mullin, K.A. Cliffe, Symmetry breaking and the onset of time dependence in fluid mechanical systems, in: S. Sarkar (Ed.), Nonlinear Phenomena and Chaos, Adam Hilger, Bristol, 1986, pp. 96–112.
24. J. Shen Efficient spectral-Galerkin method. I. Direct solvers for second-and fourth-order equations by using Legendre polynomials SIAM J. Sci. Comput. 15 1994 1489 1505
25. J. Shen, Efficient Chebyshev–Legendre Galerkin methods for elliptic problems, in: A.V. Ilin, R. Scott (Eds.), Proceedings of ICOSAHOM’95, Houston J. Math. (1996) 233–240.
26. J. Shen Efficient spectral-Galerkin methods. III. Polar and cylindrical geometries SIAM J. Sci. Comput. 18 1997 1583 1604
27. J.L. Stevens J.M. Lopez B.J. Cantwell Oscillatory flow states in an enclosed cylinder with a rotating end-wall J. Fluid Mech. 389 1999 101 118
28. G.G. Stokes On the effect of the internal friction of fluids on the motion of pendulums Trans. Camb. Phil. Soc. 9 1851 8
29. J.W. Swift K. Wiesenfeld Suppression of period doubling in symmetric systems Phys. Rev. Lett. 52 1984 705 708
30. J. van Kan A second-order accurate pressure correction scheme for viscous incompressible flow SIAM J. Sci. Stat. Comput. 7 1986 870 891
31. J. von Stamm T. Buzug G. Pfister Frequency locking in axisymmetric Taylor–Couette flow Phys. Lett. A 194 1994 173 178
32. J. von Stamm U. Gerdts T. Buzug G. Pfister Symmetry breaking and period doubling on a torus in the VLF regime in Taylor–Couette flow Phys. Rev. E 54 5 1996 4938 4957
33. A.Y. Weisberg I.G. Kevrekidis A.J. Smits Delaying transition in Taylor–Couette flow with axial motion of the inner cylinder J. Fluid Mech. 348 1997 141 151