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

被引:28
作者
Abshagen, J [1 ]
Lopez, JM
Marques, F
Pfister, G
机构
[1] Univ Kiel, Inst Expt & Appl Phys, D-24105 Kiel, Germany
[2] Arizona State Univ, Dept Math & Stat, Tempe, AZ 85287 USA
[3] Univ Politecn Cataluna, Dept Fis Aplicada, ES-08034 Barcelona, Spain
关键词
D O I
10.1017/S0022112005005811
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
We report on the results of a combined experimental and numerical study on mode interactions of rotating waves in Taylor-Couette flow. Our work shows that rotating waves which originate at a Hopf bifurcation from the steady axisymmetric Taylor vortex flow interact with this axisymmetric flow in a codimension-two fold-Hopf bifurcation. This interaction gives rise to an (unstable) low-frequency modulated wave via a subcritical Neimark-Sacker bifurcation from the rotating wave. At higher Reynolds numbers, a complicated mode interation between stable modulated waves originating at a different Neimark-Sacker bifurcation and a pair of symmetrically related rotating waves that originate at a cyclic pitchfork bifurcation is found to organize complex Z(2)-symmetry breaking of rotating waves via global bifurcations. In addition to symmetry breaking of rotating waves via a (local) cyclic pitchfork bifurcation, we found symmetry breaking of modulated waves via a saddle-node-infinite-period (SNIP) global bifurcation. Tracing these local and global bifurcation curves in Reynolds number/aspect ratio parameter space toward their apparant merging point, unexpected complexity arises in the bifurcation structure involving non-symmetric two-tori undergoing saddle-loop homoclinic bifurcations. The close agreement between the numerics and the experiment is indicative of the robustness of the observed complex dynamics.
引用
收藏
页码:269 / 299
页数:31
相关论文
共 40 条
[1]   Symmetry breaking via global bifurcations of modulated rotating waves in hydrodynamics [J].
Abshagen, J ;
Lopez, JM ;
Marques, F ;
Pfister, G .
PHYSICAL REVIEW LETTERS, 2005, 94 (07)
[2]   Gluing bifurcations in a dynamically complicated extended flow [J].
Abshagen, J ;
Pfister, G ;
Mullin, T .
PHYSICAL REVIEW LETTERS, 2001, 87 (22) :224501-224501
[3]  
[Anonymous], 1993, NATURE CHAOS
[4]   BIFURCATION PHENOMENA IN STEADY FLOWS OF A VISCOUS-FLUID .2. EXPERIMENTS [J].
BENJAMIN, TB .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1978, 359 (1696) :27-&
[5]   BIFURCATION PHENOMENA IN STEADY FLOWS OF A VISCOUS-FLUID .1. THEORY [J].
BENJAMIN, TB .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1978, 359 (1696) :1-26
[6]   NOTES ON THE MULTIPLICITY OF FLOWS IN THE TAYLOR EXPERIMENT [J].
BENJAMIN, TB ;
MULLIN, T .
JOURNAL OF FLUID MECHANICS, 1982, 121 (AUG) :219-230
[7]   Modulated rotating waves in an enclosed swirling flow [J].
Blackburn, HM ;
Lopez, JM .
JOURNAL OF FLUID MECHANICS, 2002, 465 :33-58
[8]  
Chossat P., 1994, COUETTE TAYLOR PROBL
[9]   TRANSITION IN CIRCULAR COUETTE FLOW [J].
COLES, D .
JOURNAL OF FLUID MECHANICS, 1965, 21 :385-&
[10]  
CRAWFORD JD, 1991, ANNU REV FLUID MECH, V23, P341, DOI 10.1146/annurev.fluid.23.1.341