This monograph presents a systematic and unified approach to the non-linear stability problem and transitions in the Couette-Taylor problem, by the means of analytic and constructive methods. The most "elementary" one-parameter theory is first presented. More complex situations are then analyzed (mode interactions, imperfections, non-spatially periodic patterns). The whole analysis is based on the mathematically rigorous theory of centre manifold and normal forms, and symmetries are fully taken into account. These methods ...
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This monograph presents a systematic and unified approach to the non-linear stability problem and transitions in the Couette-Taylor problem, by the means of analytic and constructive methods. The most "elementary" one-parameter theory is first presented. More complex situations are then analyzed (mode interactions, imperfections, non-spatially periodic patterns). The whole analysis is based on the mathematically rigorous theory of centre manifold and normal forms, and symmetries are fully taken into account. These methods are very general and can be applied to other hydrodynamical instabilities, or more generally to physical problems modelled by partial differential equations.
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