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

• Published in: Fluid dynamics Vol. 44; no. 6; pp. 813 - 822
• Main Authors: Morshneva, I. V., Ovchinnikova, S. N.
• Format: Journal Article
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01.12.2009
• Subjects: Amplitudes; Bifurcations; Classical and Continuum Physics; Classical Mechanics; Dynamical systems; Engineering Fluid Dynamics; Fluid dynamics; Fluid- and Aerodynamics; Intersections; Manifolds; Mathematical analysis; Physics; Physics and Astronomy; Symmetry; INW, North Pacific, Kuroshio Extension Current, Bifurcation Point; neutral curves; resonances; amplitude equations; bifurcation of codimension 2
• ISSN: 0015-4628; 1573-8507
• DOI: 10.1134/S0015462809060039

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.