Parametric instability in periodically perturbed dynamos


Parametric instability in periodically perturbed dynamos

Giesecke, A.; Stefani, F.; Herault, J.

We examine kinematic dynamo action driven by an axisymmetric large scale flow that is superimposed with an azimuthally propagating non-axisymmetric perturbation with a frequency ω. Although we apply a rather simple large scale velocity field, our simulations exhibit a complex behavior with oscillating and azimuthally drifting eigenmodes as well as stationary regimes. Within these non-oscillating regimes we find parametric resonances characterized by a considerable enhancement of dynamo action and by a locking of the phase of the magnetic field to the pattern of the perturbation. We find an approximate fulfillment of the relationship between the resonant frequency ωres of the disturbed system and the eigenfrequency ω0 of the undisturbed system given by ωres = 2 ω0 which is known from paradigmatic rotating mechanical systems and our prior study [Giesecke et al., Phys. Rev. E, 86, 066303 (2012)]. We find further -- broader -- regimes with weaker enhancement of the growth rates but without phase locking. However, this amplification regime arises only in case of a basic (i.e. unperturbed) state consisting of several different eigenmodes with rather close growth rates. Qualitatively, these observations can be explained in terms of a simple low dimensional model for the magnetic field amplitude that is derived using Floquet theory.

Keywords: Dynamo; Instability; Parametric Resonance

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Publ.-Id: 25414