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Interfacial waves arising in a two-phase swirling flow driven by a low-frequency rotating magnetic field (RMF) are studied. At low RMF frequencies, of the order of 1-10 Hz, the oscillatory part of the induced Lorenz force becomes comparable to the time-averaged one, and cannot be neglected. In particular, when free surfaces or two-liquid stably stratified systems are subject to a low-frequency RMF, induced pressure variations necessarily excite free-surface/interfacial waves, which can improve mass transfer in different metallurgical processes. In this paper, we formulate a linear wave model and derive explicit analytical solutions predicting RMF-driven wave patterns that closely resemble hyperbolic paraboloids. These theoretical predictions are validated against experiments based on a non-intrusive acoustic measurement technique, which measures liquid-liquid interface elevations in a two-phase KOH-GaInSn stably stratified system. A good quantitative agreement is found for non-resonant wave responses in the vicinity of the fundamental resonance frequency. The experiments reveal the additional excitation of several higher harmonics superimposing the fundamental wave oscillation, which are visible even in the linear wave regime.

We present results on the synchronization of the helicity in a liquid-metal Rayleigh-B\'enard (RB) experiment under the influence of a tide-like electromagnetic forcing with azimuthal wavenumber m=2. We show that for a critical forcing strength the typical Large Scale Circulation (LSC) in the cylindrical vessel of aspect ratio unity is entrained by the period of the tide-like forcing, leading to synchronized helicity oscillations with opposite signs in two half-spaces. The obtained experimental results are consistent with and supported by numerical simulations. A similar entrainment mechanism for the helicity in the solar tachocline may be responsible for the astonishing synchronization of the solar dynamo by the 11.07-year triple synodic alignment cycle of the tidally dominant planets Venus, Earth and Jupiter.

We conduct magnetic spherical Couette (MSC) flow experiments in the return flow instability regime with GaInSn as the working fluid, and the ratio of the inner to the outer sphere radii $r_{\rm i}/r_{\rm o} = 0.5$, the Reynolds number ${\rm Re} = 1000$, and the Hartmann number ${\rm Ha} \in [27.5,40]$. Rotating waves with different azimuthal wavenumbers $m \in \{2, 3, 4\}$ manifest in certain ranges of ${\rm Ha}$ in the experiments, depending on whether the values of ${\rm Ha}$ were fixed or varied from different initial values. These observations demonstrate the multistability of rotating waves, which we attribute to the dynamical system representing the state of the MSC flow tending to move along the same solution branch of the bifurcation diagram when ${\rm Ha}$ is varied. In experiments with both fixed and varying ${\rm Ha}$, the rotation frequencies of the rotating waves are consistent with the results of nonlinear stability analysis. A brief numerical investigation shows that differences in the azimuthal wavenumbers of the rotating waves that develop in the flow also depend on the azimuthal modes that are initially excited.

We show and compare numerical and experimental results on the electromagnetic generation of a tide-like flow structure in a cylindrical vessel which is filled with the eutectic liquid metal alloy GaInSn. Fields of various strengths and frequencies are applied to drive liquid metal flows. The impact of the field variations on amplitude and structure of the flows is investigated. The results represent the basis for a future Rayleigh-B\'enard experiment, in which a modulated tide-like flow perturbation is expected to synchronize the typical sloshing mode of the large-scale circulation. A similar entrainment mechanism for the helicity in the Sun may be responsible for the synchronization of the solar dynamo with the alignment cycle of the tidally dominant planets Venus, Earth and Jupiter., Comment: 11 pages, 19 figure

The project DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies) conducted at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) provides a new platform for a variety of liquid sodium experiments devoted to problems of geo- and astrophysical magnetohydrodynamics. The most ambitious experiment within this project is a precession driven dynamo experiment that currently is under construction. It consists of a cylinder filled with liquid sodium that simultaneously rotates around two axes. The experiment is motivated by the idea of a precession-driven flow as a complementary energy source for the geodynamo or the ancient lunar dynamo. In the present study we address numerical and experimental examinations in order to identify parameter regions where the onset of magnetic field excitation will be most probable. Both approaches show that in the strongly nonlinear regime the flow is essentially composed of the directly forced primary Kelvin mode and higher modes in terms of standing inertial waves that arise from nonlinear self-interactions. A peculiarity is the resonance-like emergence of an axisymmetric mode that represents a double roll structure in the meridional plane, which, however, only occurs in a very limited range of the precession ratio. This axisymmetric mode turns out to be beneficial for dynamo action, and kinematic simulations of the magnetic field evolution induced by the time-averaged flow exhibit magnetic field excitation at critical magnetic Reynolds numbers around ${\rm{Rm}}^{\rm{c}}\approx 430$, which is well within the range of the planned liquid sodium experiment., Comment: 19 pages, 14 Figures, to appear in special issue on 'Natural Dynamos' (in Geophys. Astrophys. Fluid Dyn.)

We report an experimental study of the instability of a nearly-resonant Kelvin mode forced by precession in a cylindrical vessel. The instability is detected above a critical precession ratio via the appearance of peaks in the temporal power spectrum of pressure fluctuations measured at the end-walls of the cylinder. The corresponding frequencies can be grouped into frequency sets satisfying resonance conditions with the forced Kelvin mode. We show that one triad is associated with a parametric resonance of Kelvin modes. For the first time, we observe a significant frequency variation of the unstable modes with the precession ratio. We explain this frequency modification by considering a detuning mechanism due to the slowdown of the background flow. By introducing a semi-analytical model, we show that the departure of the flow from the solid body rotation leads to a modification of the dispersion relation of Kelvin modes and to a detuning of the resonance condition. Our calculations reproduce the features of experimental measurements. We also show that a second frequency set, including one very low frequency as observed in the experiment, does not exhibit the properties of a parametric resonance between Kelvin modes. Our observations suggest that it may correspond to the instability of a geostrophic mode., Comment: 26 pages, 17 figures, accepted by Phys. Rev. Fluids

We have conducted experimental measurements and numerical simulations of a precession driven flow in a cylindrical cavity. The study is dedicated to the precession dynamo experiment currently under construction at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) and aims at the evaluation of the hydrodynamic flow with respect to its ability to drive a dynamo. We focus on the strongly nonlinear regime in which the flow is essentially composed of the directly forced primary Kelvin mode and higher modes in terms of standing inertial waves arising from nonlinear self-interactions. We obtain an excellent agreement between experiment and simulation with regard to both, flow amplitudes and flow geometry. A peculiarity is the resonance-like emergence of an axisymmetric mode that represents a double roll structure in the meridional plane. Kinematic simulations of the magnetic field evolution induced by the time-averaged flow yield dynamo action at critical magnetic Reynolds numbers around ${\rm{Rm}}^{\rm{c}}\approx 430$ which is well within the range of the planned liquid sodium experiment., Comment: 5 pages, 4 figures, accepted by Phys. Rev. Lett

The Dresden sodium facility for dynamo and thermohydraulic studies (DRESDYN) is a platform for large-scale liquid sodium experiments devoted to fundamental geo- and astrophysical questions as well as to various applied problems related to the conversion and storage of energy. Its most ambitious part is a precession driven dynamo experiment comprising 8 tons of liquid sodium supposed to rotate with up to 10 Hz and to precess with up to 1 Hz. Another large-scale set-up is a Tayler-Couette experiment with a gap width of 0.2 m and a height of 2 m, whose inner cylinder rotates with up to 20 Hz. Equipped with a coil system for the generation of an axial field of up to 120 mT and two different axial currents through the center and the liquid sodium, this experiment aims at studying various versions of the magnetorotational instability and their combinations with the Tayler instability. We discuss the physical background of these two experiments and delineate the present status of their technical realization. Other installations, such as a sodium loop and a test stand for In-Service-Inspection experiments will also be sketched., Comment: 4 pages, 2 figures

The transition to turbulence in a precessing cylindrical vessel is experimentally investigated. Our measurements are performed for a { nearly-resonant} configuration with an initially laminar flow dominated by an inertial mode with azimuthal wave number $m=1$ superimposed on a solid body rotation. By increasing the precession ratio, we observe a transition from the laminar to a non-linear regime, which then breakdowns to turbulence for larger precession ratio. Our measurements show that the transition to turbulence is subcritical, with a discontinuity of the wall-pressure and the power consumption at the threshold $\epsilon_{LT}$. The turbulence is self-sustained below this threshold, describing a bifurcation diagram with a hysteresis. In this range of the control parameters, the turbulent flows can suddenly collapse after a finite duration, leading to a definitive relaminarization of the flow. The average lifetime $\langle \tau \rangle$ of the turbulence increases rapidly when $\epsilon$ tends to $\epsilon_{LT}$., Comment: 25 pages, 12 figures

The azimuthal version of the magnetorotational instability (MRI) is a non-axisymmetric instability of a hydrodynamically stable differentially rotating flow under the influence of a purely or predominantly azimuthal magnetic field. It may be of considerable importance for destabilizing accretion disks, and plays a central role in the concept of the MRI dynamo. We report the results of a liquid metal Taylor-Couette experiment that shows the occurrence of an azimuthal MRI in the expected range of Hartmann numbers., Comment: 5 pages, 5 figures, accepted at Physical Review Letters

In the last decades, the experimental study of dynamo action has made great progress. However, after the dynamo experiments in Karlsruhe and Riga, the von-Karman-Sodium (VKS) dynamo is only the third facility that has been able to demonstrate fluid flow driven self-generation of magnetic fields in a laboratory experiment. Further progress in the experimental examination of dynamo action is expected from the planned precession driven dynamo experiment that will be designed in the framework of the liquid sodium facility DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies). In this paper, we briefly present numerical models of the VKS dynamo that demonstrate the close relation between the axisymmetric field observed in that experiment and the soft iron material used for the flow driving impellers. We further show recent results of preparatory water experiments and design studies related to the precession dynamo and delineate the scientific prospects for the final set-up., Comment: Proceedings of IAUS 294 "Solar and Astrophysical Dynamos and Magnetic Activity" Editors A.G. Kosovichev, E.M. de Gouveia Dal Pino, & Y.Yan, Cambridge University Press, to appear (2013); 6 pages 4 figures

Many astrophysical phenomena (such as the slow rotation of neutron stars or the rigid rotation of the solar core) can be explained by the action of the Tayler instability of toroidal magnetic fields in the radiative zones of stars. In order to place the theory of this instability on a safe fundament it has been realized in a laboratory experiment measuring the critical field strength, the growth rates as well as the shape of the supercritical modes. A strong electrical current flows through a liquid-metal confined in a resting columnar container with an insulating outer cylinder. As the very small magnetic Prandtl number of the gallium-indium-tin alloy does not influence the critical Hartmann number of the field amplitudes, the electric currents for marginal instability can also be computed with direct numerical simulations. The results of this theoretical concept are confirmed by the experiment. Also the predicted growth rates of the order of minutes for the nonaxisymmetric perturbations are certified by the measurements. That they do not directly depend on the size of the experiment is shown as a consequence of the weakness of the applied fields and the absence of rotation., Comment: 8 pages, 5 figures, accepted by ApJ

In the current-driven, kink-type Tayler instability (TI) a sufficiently strong azimuthal magnetic field becomes unstable against non-axisymmetric perturbations. The TI has been discussed as a possible ingredient of the solar dynamo mechanism and a source of the helical structures in cosmic jets. It is also considered as a size limiting factor for liquid metal batteries. We report on a liquid metal TI experiment using a cylindrical column of the eutectic alloy GaInSn to which electrical currents of up to 8 kA are applied. We present results of external magnetic field measurements that indicate the occurrence of the TI in good agreement with numerical predictions. The interference of TI with the competing large scale convection, resulting from Joule heating, is also discussed., Comment: 4 pages, 5 figures

Recently, a new type of battery has been proposed that relies on the principle of self-assembling of a liquid metalloid positive electrode, a liquid electrolyte, and a liquid metal negative electrode. While this configuration has been claimed to allow arbitrary up-scaling, there is a size limitation of such a system due to a current-driven kink-type instability that is known as the Tayler instability. We characterize this instability in large-scale self-assembled liquid metal batteries and discuss various technical means how it can be avoided., Comment: 15 pages, 5 figures

The magnetorotational instability (MRI) is thought to play a key role in the formation of stars and black holes by sustaining the turbulence in hydrodynamically stable Keplerian accretion discs. In previous experiments the MRI was observed in a liquid metal Taylor-Couette flow at moderate Reynolds numbers by applying a helical magnetic field. The observation of this helical MRI (HMRI) was interfered with a significant Ekman pumping driven by solid end-caps that confined the instability only to a part of the Taylor-Couette cell. This paper describes the observation of the HMRI in an improved Taylor-Couette setup with the Ekman pumping significantly reduced by using split end-caps. The HMRI, which now spreads over the whole height of the cell, appears much sharper and in better agreement with numerical predictions. By analyzing various parameter dependencies we conclude that the observed HMRI represents a self-sustained global instability rather than a noise-sustained convective one., Comment: 30 pages, 22 figures, submitted to PRE

The magnetorotational instability (MRI) plays an essential role in the formation of stars and black holes. By destabilizing hydrodynamically stable Keplerian flows, the MRI triggers turbulence and enables outward transport of angular momentum in accretion discs. We present the results of a liquid metal Taylor-Couette experiment under the influence of helical magnetic fields that show typical features of MRI at Reynolds numbers of the order 1000 and Hartmann numbers of the order 10. Particular focus is laid on an improved experiment in which split end caps are used to minimize the Ekman pumping., Comment: 7 pages, 4 figures, submitted to Magnetohydrodynamics

On 11 November 1999, a self-exciting magnetic eigenfield was detected for the first time in the Riga liquid sodium dynamo experiment. We report on the long history leading to this event, and on the subsequent experimental campaigns which provided a wealth of data on the kinematic and the saturated regime of this dynamo. The present state of the theoretical understanding of both regimes is delineated, and some comparisons with other laboratory dynamo experiments are made., Comment: 8 pages, 5 figure, accepted for publication in Comptes Rendus Physique

The magnetorotational instability (MRI) plays a key role in the formation of stars and black holes, by enabling outward angular momentum transport in accretion disks. The use of combined axial and azimuthal magnetic fields allows the investigation of this effect in liquid metal flows at moderate Reynolds and Hartmann numbers. A variety of experimental results is presented showing evidence for the occurrence of the MRI in a Taylor-Couette flow using the liquid metal alloy GaInSn., Comment: 15 pages, 13 figures, submitted to New Journal of Physics

We study experimentally the flow of a liquid metal confined between differentially rotating cylinders, in the presence of externally imposed axial and azimuthal magnetic fields. For increasingly large azimuthal fields a wave-like disturbance arises, traveling along the axis of the cylinders. The wavelengths and speeds of these structures, as well as the field strengths and rotation rates at which they arise, are broadly consistent with theoretical predictions of such a traveling wave magnetorotational instability., Comment: 5 pages, 3 figures, accepted by ApJ

A recent paper [R. Hollerbach and G. Rudiger, Phys. Rev. Lett. 95, 124501 (2005)] has shown that the threshold for the onset of the magnetorotational instability (MRI) in a Taylor-Couette flow is dramatically reduced if both axial and azimuthal magnetic fields are imposed. In agreement with this prediction, we present results of a Taylor-Couette experiment with the liquid metal alloy GaInSn, showing evidence for the existence of the MRI at Reynolds numbers of order 1000 and Hartmann numbers of order 10., Comment: 4 pages, 4 figures

The three-dimensional velocity field of a propeller driven liquid metal flow is reconstructed by a contactless inductive flow tomography (CIFT). The underlying theory is presented within the framework of an integral equation system that governs the magnetic field distribution in a moving electrically conducting fluid. For small magnetic Reynolds numbers this integral equation system can be cast into a linear inverse problem for the determination of the velocity field from externally measured magnetic fields. A robust reconstruction of the large scale velocity field is already achieved by applying the external magnetic field alternately in two orthogonal directions and measuring the corresponding sets of induced magnetic fields. Kelvin's theorem is exploited to regularize the resulting velocity field by using the kinetic energy of the flow as a regularizing functional. The results of the new technique are shown to be in satisfactory agreement with ultrasonic measurements., Comment: 9 Figures; to appear in Phys. Rev E

We consider inverse problems related to the velocity reconstruction in electrically conducting fluids from externally measured magnetic fields. The underlying theory is presented in the framework of the integral equation approach to homogeneous dynamos in finite domains, which can be cast into a linear inverse problem in case that the magnetic Reynolds number is not too large. Some mathematical problems of the inversion, including the uniqueness problem in the sphere and a paradigmatic isospectrality problem for mean-field dynamos, are touched upon. For practical purposes, the inversion is carried out with the help of Tikhonov regularization using a quadratic functional of the velocity field as penalty function. For the first time, we present results of an experiment in which the three-dimensional velocity field of a propellor driven flow in a liquid metal is reconstructed by a contactless inductive measuring technique., Comment: 8 pages, submitted to "Inverse Problems in Engineering"

After the dynamo experiment in November 1999 had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed., Comment: 4 pages, 8 figures

In an experiment at the Riga sodium dynamo facility, a slowly growing magnetic field eigenmode has been detected over a period of about 15 seconds. For a slightly decreased propeller rotation rate, additional measurements showed a slow decay of this mode. The measured results correspond satisfactory with numerical predictions for the growth rates and frequencies.