720 research outputs found
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
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 . 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
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