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Experiments with a liquid metal alloy, Galinstan, are reported and show clear evidence of Alfvén wave propagation as well as resonance of Alfvén modes. Galinstan is liquid at room temperature and, although its electrical conductivity is not as large as that of liquid sodium or NaK, it has still been possible to study Alfvén waves, thanks to the use of intense magnetic fields up to 13 T. The maximal values of Lundquist number, around 60, are similar to that of the reference experimental study by Jameson [J. Fluid Mech. 19, 513 (1964)]. The generation mechanism for Alfvén waves and their reflection is studied carefully. Numerical simulations have been performed and have been able to reproduce the experimental results, despite the fact that the simulated magnetic Prandtl number was much larger than that of Galinstan. An originality of the present study is that a poloidal disturbance (magnetic and velocity fields) is generated, allowing us to track its propagation from outside the conducting domain, hence without interfering. [ABSTRACT FROM AUTHOR]

A stabilized finite element ( B, q) formulation is developed to solve the kinematic dynamo problem. As a test case, we solve the induction equation for a given solid body helical flow, embedded in a cylindrical conducting shell. This problem corresponds to the well-known Ponomarenko dynamo. It has the interesting property to have an exact dispersion relation giving the magnetic growth rate as a function of the flow properties. Therefore, it is a good benchmark to test our kinematic dynamo code. We calculated the dynamo threshold and plotted the geometry of the generated magnetic field. We also evaluated the residual error due to our stabilized formulation. [ABSTRACT FROM AUTHOR]

This paper considers dynamo action in smooth helical flows in cylindrical geometry, otherwise known as Ponomarenko dynamos, with periodic time dependence. An asymptotic framework is developed that gives growth rates and frequencies in the highly conducting limit of large magnetic Reynolds number, when modes tend to be localized on resonant stream surfaces. This theory is validated by means of numerical simulations. [ABSTRACT FROM AUTHOR]

Scale separation between the flow and the magnetic field is a common feature of natural dynamos. It has also been used in the Karlsruhe sodium experiment in which the scale of the magnetic field is roughly seven times larger than the scale of the flow [R. Stieglitz and U. Müller, “Experimental demonstration of the homogeneous two-scale dynamo,” Phys. Fluids 13, 561 (2001)]. Recently, Fauve and Pétrélis [Peyresq Lectures on Nonlinear Phenomena, edited by J. Sepulchre (World Scientific, Singapore, 2003), p. 1] have shown that the power needed to reach the dynamo threshold in a dynamo experiment increases with the scale separation in the limit of large scale separation. With a more elaborate method based on subharmonic solutions [F. Plunian and K.-H. Rädler, “Subharmonic dynamo action in the Roberts flow,” Geophys. Astrophys. Fluid Dyn. 96, 115 (2002)], we show, for the Roberts flow, the existence of an optimal scale separation for which this power is minimum. Previous results obtained by Tilgner [“A kinematic dynamo with a small scale velocity field,” Phys. Lett. A 226, 75 (1997)] with a completely different numerical method are also reconsidered here. Again, we find an optimal scale separation in terms of minimum power for dynamo action. In addition we find that this scale separation compares very well with the one derived from the subharmonic solutions method. [ABSTRACT FROM AUTHOR]

Abstract: We use a simple model of Bullard-type disc dynamo, in which the disc rotation rate is subject to harmonic oscillations, to analyze the generation of magnetic field by the parametric resonance mechanism. The problem is governed by a damped Mathieu equation. The Floquet exponents, which define the magnetic field growth rates, are calculated depending on the amplitude and frequency of the oscillations. Firstly, we show that the dynamo can be excited at significantly subcritical disc rotation rate when the latter is subject to harmonic oscillations with a certain frequency. Secondly, at supercritical mean rotation rates, the dynamo can also be suppressed but only in narrow frequency bands and at sufficiently large oscillation amplitudes. [Copyright &y& Elsevier]