Parametric instability of the helical dynamo

University of Grenoble, Grenoble, Rhône-Alpes, France
Physics of Fluids (Impact Factor: 2.03). 05/2007; 19(5):054109. DOI: 10.1063/1.2734118
Source: arXiv


We study the dynamo threshold of a helical flow made of a mean (stationary) plus a fluctuating part. Two flow geometries are studied, either (i) solid body or (ii) smooth. Two well-known resonant dynamo conditions, elaborated for stationary helical flows in the limit of large magnetic Reynolds numbers, are tested against lower magnetic Reynolds numbers and for fluctuating flows (zero mean). For a flow made of a mean plus a fluctuating part the dynamo threshold depends on the frequency and the strength of the fluctuation. The resonant dynamo conditions applied on the fluctuating (resp. mean) part seems to be a good diagnostic to predict the existence of a dynamo threshold when the fluctuation level is high (resp. low). Comment: 37 pages, 8 figures

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    • "Recent work on the cylindrical Ponomarenko dynamo shows that magnetic growth persists when the amplitudes of the helical flow has a small time-dependent (fluctuating) part. Dynamo action even can occur when the meridional and azimuthal fluctuations are slightly different functions of time, forcing the resonant curve to also change with time (Peyrot et al. 2007, 2008). Similar behaviour undoubtedly carries over to the spherical single roll dynamos we consider. "
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    ABSTRACT: This paper concerns kinematic helical dynamos in a spherical fluid body surrounded by an insulator. In particular, we examine their behaviour in the regime of large magnetic Reynolds number $\Rm$, for which dynamo action is usually concentrated upon a simple resonant stream-surface. The dynamo eigensolutions are computed numerically for two representative single-roll flows using a compact spherical harmonic decomposition and fourth-order finite-differences in radius. These solutions are then compared with the growth rates and eigenfunctions of the Gilbert and Ponty (2000) large $\Rm$ asymptotic theory. We find good agreement between the growth rates when $\Rm>10^4$, and between the eigenfunctions when $\Rm>10^5$.
    Physics of Fluids 06/2010; 22(6). DOI:10.1063/1.3453712 · 2.03 Impact Factor
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    ABSTRACT: The kinematic dynamo problem is solved in a cylindrical geometry using Galerkin expansions of the magnetic field components. The difference with the modal Galerkin analysis [L. Marié et al., Phys. Fluids 18, 017102 (2006)] concerns the weighting functions which here belong to the same set as the trial functions. The new procedure allows to determine the magnetic Reynolds number RmE for energy growth. Lower bounds on the value of RmE are derived for magnetic modes of azimuthal wavenumber m. Using a variational principle, more accurate values of RmE are obtained in the case of helical flows. It is found that the threshold value for the axisymmetric magnetic mode m=0 is slightly higher than its value for the antisymmetric mode m=1. Although excluded by Cowling's theorem the mode m=0 exhibits transient energy growth and could play a role in the nonlinear equilibration of cylindrical dynamos.
    Physics of Fluids 01/2008; 20(8):2008. DOI:10.1063/1.2972889 · 2.03 Impact Factor
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    ABSTRACT: The study of dynamo action in astrophysical objects classically involves two timescales: the slow diffusive one and the fast advective one. We investigate the possibility of field amplification on an intermediate timescale associated with time dependent modulations of the flow. We consider a simple steady configuration for which dynamo action is not realised. We study the effect of time dependent perturbations of the flow. We show that some vanishing low frequency perturbations can yield exponential growth of the magnetic field on the typical time scale of oscillation. The dynamo mechanism relies here on a parametric instability associated with transient amplification by shear flows. Consequences on natural dynamos are discussed.
    EPL (Europhysics Letters) 04/2008; 81(6). DOI:10.1209/0295-5075/81/64002 · 2.10 Impact Factor
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