TY - JOUR
T1 - Mode competition of rotating waves in reflection-symmetric Taylor-Couette flow
AU - Abshagen, J.
AU - Lopez, Juan
AU - Marques, F.
AU - Pfister, G.
PY - 2005/10/10
Y1 - 2005/10/10
N2 - 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 Z2-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.
AB - 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 Z2-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.
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U2 - 10.1017/S0022112005005811
DO - 10.1017/S0022112005005811
M3 - Article
AN - SCOPUS:26944486562
SN - 0022-1120
VL - 540
SP - 269
EP - 299
JO - journal of fluid mechanics
JF - journal of fluid mechanics
ER -