Implications of three dimensional velocity distributions on the generation of magnetic fields in the Von-K\'arm\'an-Sodium dynamo experiment.


Implications of three dimensional velocity distributions on the generation of magnetic fields in the Von-K\'arm\'an-Sodium dynamo experiment.

Giesecke, A.; Stefani, F.; Gerbeth, G.

Numerical simulations of the kinematic induction equation have been carried out in a cylindrical domain that resembles the configuration of the VKS dynamo experiment. Primary objective are investigations of non-axisymmetric source terms and their impact on the critical Reynolds number as well as onthe structure of the field geometry.

In case of an axisymmetric velocity distribution the resulting magnetic field is always determined by an azimuthal m=1-mode which is in contradiction to the experimental realization that is dominated by an axisymmetric field.

A simple non-axisymmetric contribution can be parameterized by a localized $\alpha$-effect which arises from the induction action of radially oriented helical outflow between the impeller blades that drive the flow. However, it turns out, that the amplitude of $\alpha$ which is necessary to obtain an axisymmetric field is far above realistic values.

Further potential contributions involve a time dependent non-axisymmetric velocity component in form of azimuthal drifting equatorial vortices as they have been found in water experiments. These structures provide a coupling between different field modes, but the m=1 mode still remains dominant. Resonance effects provide a strong increment of the field growthrate if the vortex drift motion proceeds phase synchronous with a drift of the magnetic field caused by equatorial symmetry braking of the velocity distribution. Presumably this phenomenon is not relevant in the experiment, as the drift of the eigenfield is very small so that resonance would require a much slower vortex drift velocity than it is observed.

So far, non-axisymmetric source terms in the induction equation are not able to explain the dominance of the m=0 mode, however it remains still possible that a quite exotic dynamo mechanism is operating which is essentially based on induction terms generated by the azimuthal variation of the permeability introduced by the ferrous impellers.

Keywords: dynamo; alpha-effect; induction; kinematic simulations

  • Lecture (Conference)
    Frontiers in Dynamo Theory, 16.-20.03.2009, Paris, France

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Publ.-Id: 12409