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Cyclic nonlinear dynamo action in a finite Taylor Couette flow

We present calculations of dynamo action in a finite Taylor-Couette configuration. The first hydrodynamic bifurcation is an imperfect pitchfork bifurcation giving rise to Taylor vortices. This flow is used in kinematic dynamo computations showing a Hopf bifurcation towards a localized magnetic structure of typical length twice as long as the velocity typical length. Using Taylor vortices and the magnetic eigenvector obtained from the kinematic regime, the nonlinear dynamo shows a striking cyclic behaviour where the symmetries with respect to the median plane play a major role.