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Resonance regimes in the neighborhood of bifurcation points of codimension 2 in the Couette-Taylor problem

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Abstract

The bifurcation in a dynamical system with cylindrical symmetry dependent on several parameters is studied with reference to the Couette-Taylor problem. Points at which two neutral curves intersect (bifurcation points of codimension 2) corresponding to several independent neutral modes are found. In the neighborhood of the bifurcation points of codimension 2 the interaction of these modes can be described by a system of amplitude equations on the central manifold. If the neutral modes are nonrotationally symmetrical, there exist seven different resonance states that influence the cubic terms of the amplitude system. For the resonances Res 0 and Res 3 the results of calculating the intersection points are presented and the conditions under which stationary regimes exist and are stable are analyzed.

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Authors
  1. I. V. Morshneva
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  2. S. N. Ovchinnikova
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Additional information

Original Russian Text © I.V. Morshneva, S.N. Ovchinnikova, 2009, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2009, Vol. 44, No. 6, pp. 21–31.

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Morshneva, I.V., Ovchinnikova, S.N. Resonance regimes in the neighborhood of bifurcation points of codimension 2 in the Couette-Taylor problem. Fluid Dyn 44, 813–822 (2009). https://doi.org/10.1134/S0015462809060039

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  • DOI: https://doi.org/10.1134/S0015462809060039

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