39 research outputs found
Role of soft-iron impellers on the mode selection in the VKS dynamo experiment
A crucial point for the understanding of the von-K\'arm\'an-Sodium (VKS)
dynamo experiment is the influence of soft-iron impellers. We present numerical
simulations of a VKS-like dynamo with a localized permeability distribution
that resembles the shape of the flow driving impellers. It is shown that the
presence of soft-iron material essentially determines the dynamo process in the
VKS experiment. % An axisymmetric magnetic field mode can be explained by the
combined action of the soft-iron disk and a rather small -effect
parametrizing the induction effects of unresolved small scale flow
fluctuations
Long term time dependent frequency analysis of chaotic waves in the weakly magnetized spherical Couette system
The long therm behavior of chaotic flows is investigated by means of time
dependent frequency analysis. The system under test consists of an electrically
conducting fluid, confined between two differentially rotating spheres. The
spherical setup is exposed to an axial magnetic field. The classical Fourier
Transform method provides a first estimation of the time dependence of the
frequencies associated to the flow, as well as its volume-averaged properties.
It is however unable to detect strange attractors close to regular solutions in
the Feigenbaum as well as Newhouse-Ruelle-Takens bifurcation scenarios. It is
shown that Laskar's frequency algorithm is sufficiently accurate to identify
these strange attractors and thus is an efficient tool for classification of
chaotic flows in high dimensional dynamical systems. Our analysis of several
chaotic solutions, obtained at different magnetic field strengths, reveals a
strong robustness of the main frequency of the flow. This frequency is
associated to an azimuthal drift and it is very close to the frequency of the
underlying unstable rotating wave. In contrast, the main frequency of
volume-averaged properties can vary almost one order of magnitude as the
magnetic forcing is decreased. We conclude that, at the moderate differential
rotation considered, unstable rotating waves provide a good description of the
variation of the main time scale of any flow with respective variations in the
magnetic field.Comment: 12 pages, 9 figures and 2 tables. Accepted for Physica D: Nonlinear
Phenomen
Four-frequency solution in a magnetohydrodynamic Couette flow as a consequence of azimuthal symmetry breaking
The occurrence of magnetohydrodynamic (MHD) quasiperiodic flows with four
fundamental frequencies in differentially rotating spherical geometry is
understood in terms of a sequence of bifurcations breaking the azimuthal
symmetry of the flow as the applied magnetic field strength is varied. These
flows originate from unstable periodic and quasiperiodic states with broken
equatorial symmetry but having four-fold azimuthal symmetry. A posterior
bifurcation gives rise to two-fold symmetric quasiperiodic states, with three
fundamental frequencies, and a further bifurcation to a four-frequency
quasiperiodic state which has lost all the spatial symmetries. This bifurcation
scenario may be favoured when differential rotation is increased and periodic
flows with -fold azimuthal symmetry, being product of several prime
numbers, emerge at sufficiently large magnetic field.Comment: 8 pages, 7 figures, published in Phys. Rev. Le
Chaotic wave dynamics in weakly magnetised spherical Couette flows
Direct numerical simulations of a liquid metal filling the gap between two
concentric spheres are presented. The flow is governed by the interplay between
the rotation of the inner sphere (measured by the Reynolds number Re) and a
weak externally applied axial magnetic field (measured by the Hartmann number
Ha). By varying the latter a rich variety of flow features, both in terms of
spatial symmetry and temporal dependence, is obtained. Flows with two or three
independent frequencies describing their time evolution are found as a result
of Hopf bifurcations. They are stable on a sufficiently large interval of
Hartmann numbers where regions of multistability of two, three and even four
types of these different flows are detected. The temporal character of the
solutions is analysed by means of an accurate frequency analysis and Poincar\'e
sections. An unstable branch of flows undergoing a period doubling cascade and
frequency locking of three-frequency solutions is described as well.Comment: 32 pages, 12 figures and 3 table
Chaotic wave dynamics in weakly magnetized spherical Couette flows
Direct numerical simulations of a liquid metal filling the gap between two concentric spheres are presented. The flow is governed by the interplay between the rotation of the inner sphere (measured by the Reynolds number ¿¿) and a weak externally applied axial magnetic field (measured by the Hartmann number Ha
). By varying the latter, a rich variety of flow features, both in terms of spatial symmetry and temporal dependence, is obtained. Flows with two or three independent frequencies describing their time evolution are found as a result of Hopf bifurcations. They are stable on a sufficiently large interval of Hartmann numbers where regions of multistability of two, three, and even four types of these different flows are detected. The temporal character of the solutions is analyzed by means of an accurate frequency analysis and Poincaré sections. An unstable branch of flows undergoing a period doubling cascade and frequency locking of three-frequency solutions is described as well.
One of the paradigms of magnetohydrodynamic flows in spherical geometry is the magnetized spherical Couette flow. An electrically conducting liquid is confined between two differentially rotating spheres and is subjected to a magnetic field. Despite its simplicity, this model gives rise to a rich variety of instabilities, and it is also important from an astrophysical point of view. The present study advances the knowledge of the dynamics of this problem by describing it in terms of dynamical systems theory, a rigorous mathematical way to understand time dependent behavior of natural systems.Peer ReviewedPostprint (author's final draft
High dimensional tori and chaotic and intermittent transients in magnetohydrodynamic Couette flows
The magnetised spherical Couette (MSC) problem, a three dimensional magnetohydrodynamic paradigmatic model in geo- and astrophysics, is considered to investigate bifurcations to high-dimensional invariant tori and chaotic flows in large scale dissipative dynamical systems with symmetry. The main goal of the present study is to elucidate the origin of chaotic transients and intermittent behaviour from two different sequences of Hopf bifurcations involving invariant tori with four fundamental frequencies, which may be resonant. Numerical evidence of the existence of a crisis event destroying chaotic attractors and giving rise to the chaotic transients is provided. It is also shown that unstable invariant tori take part in the time evolution of these chaotic transients. For one sequence of bifurcations, the study demonstrates that chaotic transients display on–off intermittent behaviour. A possible explanatory mechanism is discussed.Peer ReviewedPostprint (published version
Intermittent chaotic flows in the weakly magnetised spherical Couette system
Experiments on the magnetised spherical Couette system are presently being carried out at Helmholtz-Zentrum Dresden-Rossendorf (HZDR). A liquid metal (GaInSn) is confined within two differentially rotating spheres and exposed to a magnetic field parallel to the axis of rotation. Intermittent chaotic flows, corresponding to the radial jet instability, are described. The relation of these chaotic flows with unstable regular (periodic and quasiperiodic) solutions obtained at the same range of parameters is investigated.Peer ReviewedPostprint (published version
Impact of time-dependent non-axisymmetric velocity perturbations on dynamo action of von-K\'arm\'an-like flows
We have performed 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 non-axisymmetric 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 model
water experiment conducted at the University of Navarra in Pamplona, Spain. Our
simulations show that the interactions of azimuthally drifting flow
perturbations with the fundamental drift of the magnetic eigenmode (caused by
the inevitable equatorial symmetry breaking of the basic flow) 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
() vortex-like 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 an spectral exceptional point where eigenvalues
(growth-rates and frequencies) and eigenfunctions of two previously independent
modes collapse.Comment: 14 pages, 14 Figures. Minor changes to match the published versio