Modulated rotating waves in the magnetized spherical Couette system

We present a study devoted to a detailed description of modulated rotating waves (MRW) in the magnetized spherical Couette system. The set-up consists of a liquid metal confined between two differentially rotating spheres and subjected to an axially applied magnetic field. When the magnetic field strength is varied, several branches of MRW are obtained by means of three dimensional direct numerical simulations (DNS). The MRW originate from parent branches of rotating waves (RW) and are classified according to Rand's (Arch. Ration. Mech. Anal 79:1-37, 182) and Coughling & Marcus (J. Fluid Mech. 234:1-18,1992) theoretical description. We have found relatively large intervals of multistability of MRW at low magnetic field, corresponding to the radial jet instability known from previous studies. However, at larger magnetic field, corresponding to the return flow regime, the stability intervals of MRW are very narrow and thus they are unlikely to be found without detailed knowledge of their bifurcation point. A careful analysis of the spatio-temporal symmetries of the most energetic modes involved in the different classes of MRW will allow in the future a comparison with the HEDGEHOG experiment, a magnetized spherical Couette device hosted at the Helmholtz-Zentrum Dresden-Rossendorf.Comment: Contains 3 tables and 8 figures. Published in the Journal of Nonlinear Scienc

Triadic resonances in non-linear simulations of a fluid flow in a precessing cylinder

We present results from three-dimensional non-linear hydrodynamic simulations of a precession driven flow in cylindrical geometry. The simulations are motivated by a dynamo experiment currently under development at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) in which the possibility of generating a magnetohydrodynamic dynamo will be investigated in a cylinder filled with liquid sodium and simultaneously rotating around two axes. In this study, we focus on the emergence of non-axisymmetric time-dependent flow structures in terms of inertial waves which - in cylindrical geometry - form so-called Kelvin modes. For a precession ratio ${\rm{Po}}=\Omega_p/\Omega_c=0.014$ the amplitude of the forced Kelvin mode reaches up to one fourth of the rotation velocity of the cylindrical container confirming that precession provides a rather efficient flow driving mechanism even at moderate values of ${\rm{Po}}$. More relevant for dynamo action might be free Kelvin modes with higher azimuthal wave number. These free Kelvin modes are triggered by non-linear interactions and may constitute a triadic resonance with the fundamental forced mode when the height of the container matches their axial wave lengths. Our simulations reveal triadic resonances at aspect ratios close to those predicted by the linear theory except around the primary resonance of the forced mode. In that regime we still identify various free Kelvin modes, however, all of them exhibit a retrograde drift around the symmetry axis of the cylinder and none of them can be assigned to a triadic resonance. The amplitudes of the free Kelvin modes always remain below the forced mode but may reach up to 6% of the of the container's angular velocity. The properties of the free Kelvin modes will be used in future simulations of the magnetic induction equation to investigate their ability to provide for dynamo action.Comment: 26 pages, 14 figures, submitted to New J. Phy

Electromagnetic induction in non-uniform domains

Kinematic simulations of the induction equation are carried out for different setups suitable for the von-K\'arm\'an-Sodium (VKS) dynamo experiment. Material properties of the flow driving impellers are considered by means of high conducting and high permeability disks that are present in a cylindrical volume filled with a conducting fluid. Two entirely different numerical codes are mutually validated by showing quantitative agreement on Ohmic decay and kinematic dynamo problems using various configurations and physical parameters. Field geometry and growth rates are strongly modified by the material properties of the disks even if the high permeability/high conductivity material is localized within a quite thin region. In contrast the influence of external boundary conditions remains small. Utilizing a VKS like mean fluid flow and high permeability disks yields a reduction of the critical magnetic Reynolds number for the onset of dynamo action of the simplest non-axisymmetric field mode. However this decrease is not sufficient to become relevant in the VKS experiment. Furthermore, the reduction of Rm_c is essentially influenced by tiny changes in the flow configuration so that the result is not very robust against small modifications of setup and properties of turbulence

Induction in a von Karman flow driven by ferromagnetic impellers

We study magnetohydrodynamics in a von K\'arm\'an flow driven by the rotation of impellers made of material with varying electrical conductivity and magnetic permeability. Gallium is the working fluid and magnetic Reynolds numbers of order unity are achieved. We find that specific induction effects arise when the impeller's electric and magnetic characteristics differ from that of the fluid. Implications in regards to the VKS dynamo are discussed.Comment: 14 pages, 7 figure

Towards a precession driven dynamo experiment

The most ambitious project within the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) is the set-up of a precession-driven dynamo experiment. After discussing the scientific background and some results of water pre-experiments and numerical predictions, we focus on the numerous structural and design problems of the machine. We also outline the progress of the building's construction, and the status of some other experiments that are planned in the framework of DRESDYN.Comment: 9 pages, 6 figures, submitted to Magnetohydrodynamic

Impact of time-dependent nonaxisymmetric velocity perturbations on dynamo action of von Kármán-like flows

We present numerical simulations of the kinematic induction equation in order to examine the dynamo efficiency of an axisymmetric von K´arm´an–like flow subject to time-dependent nonaxisymmetric velocity perturbations. The numerical model is based on the setup of the French von K´arm´an-sodium dynamo (VKS) and on the flow measurements from a water experiment conducted at the University of Navarra in Pamplona, Spain. The principal experimental observations that are modeled in our simulations are nonaxisymmetric vortexlike structures which perform an azimuthal drift motion in the equatorial plane. Our simulations show that the interactions of these periodic flow perturbations with the fundamental drift of the magnetic eigenmode (including the special case of nondrifting fields) essentially determine the temporal behavior of the dynamo state.We find two distinct regimes of dynamo action that depend on the (prescribed) drift frequency of an (m = 2) vortexlike flow perturbation. For comparatively slowly drifting vortices we observe a narrow window with enhanced growth rates and a drift of the magnetic eigenmode that is synchronized with the perturbation drift. The resonance-like enhancement of the growth rates takes place when the vortex drift frequency roughly equals the drift frequency of the magnetic eigenmode in the unperturbed system. Outside of this small window, the field generation is hampered compared to the unperturbed case, and the field amplitude of the magnetic eigenmode is modulated with approximately twice the vortex drift frequency. The abrupt transition between the resonant regime and the modulated regime is identified as a spectral exceptional point where eigenvalues (growth rates and frequencies) and eigenfunctions of two previously independent modes collapse. In the actual configuration the drift frequencies of the velocity perturbations that are observed in the water experiment are much larger than the fundamental drift frequency of the magnetic eigenmode that is obtained from our numerical simulations. Hence, we conclude that the fulfillment of the resonance condition might be unlikely in present day dynamo experiments. However, a possibility to increase the dynamo efficiency in the VKS experiment might be realized by an application of holes or fingers on the outer boundary in the equatorial plane. These mechanical distortions provoke an anchorage of the vortices at fixed positions thus allowing an adjustment of the temporal behavior of the nonaxisymmetric flow perturbations