Christophe Gissinger

Effect of magnetic boundary conditions on the dynamo threshold of von Kármán swirling flows

We study the effect of different boundary conditions on the kinematic dynamo threshold of von Karman type swirling flows in a cylindrical geometry. Using an analytical test flow, we model different boundary conditions: insulating walls all over the flow, effect of sodium at rest on the cylinder side boundary, effect of sodium behind the impellers, effect of impellers or side wall made of a high-magnetic-permeability material. We find that using high-magnetic-permeability boundary conditions decreases the dynamo threshold, the minimum being achieved when they are implemented all over the flow.

A numerical model of the VKS experiment

We present numerical simulations of the magnetic field generated by the flow of liquid sodium driven by two counter-rotating impellers (VKS experiment). Using a kinematic code in cylindrical geometry, it is shown that different magnetic modes can be generated depending on the flow configuration. While the time-averaged axisymmetric mean flow generates an equatorial dipole, our simulations show that an axial field of either dipolar or quadrupolar symmetry can be generated by taking into account non-axisymmetric components of the flow. Moreover, we show that by breaking a symmetry of the flow, the magnetic field becomes oscillatory. This leads to reversals of the axial dipole polarity, involving a competition with the quadrupolar component.

Dynamo regimes and transitions in the VKS experiment

Abstract. The Von Kármán Sodium experiment yields a variety of dynamo regimes, when asymmetry is imparted to the flow by rotating impellers at different speed F1 and F2. We show that as the intensity of forcing, measured as F1+F2, is increased, the transition to a self-sustained magnetic field is always observed via a supercritical bifurcation to a stationary state. For some values of the asymmetry parameter θ = (F1–F2)/(F1+F2), time dependent dynamo regimes develop. They are observed either when the forcing is increased for a given value of asymmetry, or when the amount of asymmetry is varied at sufficiently high forcing. Two qualitatively different transitions between oscillatory and stationary regimes are reported, involving or not a strong divergence of the period of oscillations. These transitions can be interpreted using a low dimensional model based on the interactions of two dynamo modes.

Morphology of field reversals in turbulent dynamos

We show that the modes involved in the dynamics of reversals of the magnetic field generated by the flow of an electrically conducting fluid in a spherical domain, strongly depend on the magnetic Prandtl number Pm, i.e., the ratio between viscous and magnetic diffusivities. For Pm~1, the axial dipolar field reverses in the presence of a strong equatorial dipolar component, whereas for Pm<0.5, field reversals mostly involve axisymmetric modes, axial magnetic dipole and quadrupole coupled through a broken symmetry of the flow. Using symmetry arguments, we write a dynamical system for these three modes that qualitatively reproduces the main features of the reversals observed in direct simulations for small Pm.

The role of boundaries in the magnetorotational instability

In this paper, we investigate numerically the flow of an electrically conducting fluid in a cylindrical Taylor-Couette flow when an axial magnetic field is applied. To minimize Ekman recirculation due to vertical no-slip boundaries, two independently rotating rings are used at the vertical endcaps. This configuration reproduces setup used in laboratory experiments aiming to observe the magnetorotational instability (MRI). Our 3D global simulations show that the nature of the bifurcation, the non-linear saturation, and the structure of axisymmetric MRI modes are significantly affected by the presence of boundaries. In addition, large scale non-axisymmetric modes are obtained when the applied field is sufficiently strong. We show that these modes are related to Kelvin-Helmholtz destabilization of a free Shercliff shear layer created by the combined action of the applied field and the rotating rings at the endcaps. Finally, we compare our numerical simulations to recent experimental results obtained in the P...

Bypassing Cowling's Theorem in Axisymmetric Fluid Dynamos

We present a numerical study of the magnetic field generated by an axisymmetrically forced flow in a spherical domain. We show that, even in the absence of nonaxisymmetric velocity fluctuations, a mean magnetic field with a dominant axisymmetric dipolar component can be generated via a secondary bifurcation from an equatorial dipole. We understand the dynamical behaviors that result from the interaction of equatorial and axial dipolar modes using simple model equations for their amplitudes derived from symmetry arguments.

Direct numerical simulations of the galactic dynamo in the kinematic growing phase

ABSTRACT We present kinematic simulations of a galactic dynamo model based on the largescale differential rotation and the small scale helical fluctuations due to supernova ex-plosions. We report for the first time direct numerical simulations of the full galacticdynamo using an unparameterized global approach. We argue that the scale of helicityinjection is large enough to be directly resolved rather than parameterized. While theactual superbubble characteristics can only be approached, we show that numericalsimulations yield magnetic structures which are close both to the observations and tothe previous parameterized mean field models. In particular, the quadrupolar symme-try and the spiraling properties of the field are reproduced. Moreover, our simulationsshow that the presence of a vertical inflow plays an essential role to increase the mag-netic growth rate. This observation could indicate an important role of the downwardflow (possibly linked with galactic fountains) in sustaining galactic magnetic fields.Key words: Dynamo – Galaxies – Supernovae – Superbubbles.

Dipole-quadrupole dynamics during magnetic field reversals

The shape and the dynamics of reversals of the magnetic field in a turbulent dynamo experiment are investigated. We report the evolution of the dipolar and the quadrupolar parts of the magnetic field in the VKS experiment, and show that the experimental results are in good agreement with the predictions of a recent model of reversals: when the dipole reverses, part of the magnetic energy is transferred to the quadrupole, reversals begin with a slow decay of the dipole and are followed by a fast recovery, together with an overshoot of the dipole. Random reversals are observed at the borderline between stationary and oscillatory dynamos.

The Taylor-vortex dynamo

The generation of a magnetic field by dynamo action in a Taylor-vortex flow is investigated numerically. We first discuss how the Taylor vortices generate a spatially subharmonic dynamo, for which the axial wavelength of the magnetic field is twice the one of the flow pattern. Then, we investigate the influence of the Reynolds number and the turbulent fluctuations on the structure and the onset of the Taylor-Couette dynamo. Finally, based on the subharmonic nature of this dynamo, we propose new configurations which could be relevant for laboratory experiments.

Instability in electromagnetically driven flows. II

The magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel is investigated numerically. For sufficiently large magnetic Reynolds numberRm, or if a large enough pressure gradient is externally applied, the system undergoes an instability in which the flow rate in the channel dramatically drops from synchronism with the wave to much smaller velocities. This transition takes the form of a saddle-node bifurcation for the time-averaged quantities. In this first paper, we characterize the bifurcation and study the stability of the flow as a function of several parameters. We show that the bifurcation of the flow involves a bistability between Poiseuille-like and Hartman-like regimes and relies on magnetic flux expulsion. Based on this observation, new predictions are made for the occurrence of this stalling instability.