DOI

1

Instability in electromagnetically driven flows. II - Imazio, Paola Rodriguez and Gissinger, Christophe

PHYSICS OF FLUIDS 28, (2016)

Abstract : In a previous paper, we have reported numerical simulations of the magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel, at low Reynolds number. It was shown that the stalling of such induction pump is strongly related to magnetic flux expulsion. In the present article, we show that for larger hydrodynamic Reynolds number, and with more realistic boundary conditions, this instability takes the form of a large axisymmetric vortex flow in the (r, z)-plane, in which the fluid is locally pumped in the direction opposite to the one of the magnetic field. Close to the marginal stability of this vortex flow, a low-frequency pulsation is generated. Finally, these results are compared to theoretical predictions and are discussed within the framework of experimental annular linear induction electromagnetic pumps. (C) 2016 AIP Publishing LLC.

PHYSICS OF FLUIDS 28, (2016)

LPS

Abstract : In a previous paper, we have reported numerical simulations of the magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel, at low Reynolds number. It was shown that the stalling of such induction pump is strongly related to magnetic flux expulsion. In the present article, we show that for larger hydrodynamic Reynolds number, and with more realistic boundary conditions, this instability takes the form of a large axisymmetric vortex flow in the (r, z)-plane, in which the fluid is locally pumped in the direction opposite to the one of the magnetic field. Close to the marginal stability of this vortex flow, a low-frequency pulsation is generated. Finally, these results are compared to theoretical predictions and are discussed within the framework of experimental annular linear induction electromagnetic pumps. (C) 2016 AIP Publishing LLC.

DOI

2

Instability in electromagnetically driven flows. I - Gissinger, Christophe and Imazio, Paola Rodriguez and Fauve, Stephan

PHYSICS OF FLUIDS 28, (2016)

Abstract : The magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel is investigated numerically. For sufficiently large magnetic Reynolds number Rm, 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. (C) 2016 AIP Publishing LLC.

PHYSICS OF FLUIDS 28, (2016)

LPS

Abstract : The magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel is investigated numerically. For sufficiently large magnetic Reynolds number Rm, 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. (C) 2016 AIP Publishing LLC.

DOI

3

Fluctuations of Electrical Conductivity: A New Source for Astrophysical Magnetic Fields - Petrelis, F. and Alexakis, A. and Gissinger, C.

PHYSICAL REVIEW LETTERS 116, (2016)

Abstract : We consider the generation of a magnetic field by the flow of a fluid for which the electrical conductivity is nonuniform. A new amplification mechanism is found which leads to dynamo action for flows much simpler than those considered so far. In particular, the fluctuations of the electrical conductivity provide a way to bypass antidynamo theorems. For astrophysical objects, we show through three-dimensional global numerical simulations that the temperature-driven fluctuations of the electrical conductivity can amplify an otherwise decaying large scale equatorial dipolar field. This effect could play a role for the generation of the unusually tilted magnetic field of the iced giants Neptune and Uranus.

PHYSICAL REVIEW LETTERS 116, (2016)

LPS

Abstract : We consider the generation of a magnetic field by the flow of a fluid for which the electrical conductivity is nonuniform. A new amplification mechanism is found which leads to dynamo action for flows much simpler than those considered so far. In particular, the fluctuations of the electrical conductivity provide a way to bypass antidynamo theorems. For astrophysical objects, we show through three-dimensional global numerical simulations that the temperature-driven fluctuations of the electrical conductivity can amplify an otherwise decaying large scale equatorial dipolar field. This effect could play a role for the generation of the unusually tilted magnetic field of the iced giants Neptune and Uranus.

DOI

4

Wave-induced motion of magnetic spheres - Gissinger, Christophe

EPL 112, (2015)

Abstract : We report an experimental study of the motion of magnetized beads driven by a travelling-wave magnetic field. For sufficiently large wave speed, we report the existence of a backward motion, in which the sphere can move in the direction opposite to the driving wave. We show that the transition to this new state is strongly subcritical and can lead to chaotic motion of the bead. For some parameters, this counterpropagation of the sphere can be one order of magnitude faster than the driving-wave speed. These results are understood in the framework of a model based on the interplay among solid friction, air resistance and magnetic torque. Copyright (C) EPLA, 2015

EPL 112, (2015)

LPS

Abstract : We report an experimental study of the motion of magnetized beads driven by a travelling-wave magnetic field. For sufficiently large wave speed, we report the existence of a backward motion, in which the sphere can move in the direction opposite to the driving wave. We show that the transition to this new state is strongly subcritical and can lead to chaotic motion of the bead. For some parameters, this counterpropagation of the sphere can be one order of magnitude faster than the driving-wave speed. These results are understood in the framework of a model based on the interplay among solid friction, air resistance and magnetic torque. Copyright (C) EPLA, 2015

DOI

5

The Taylor-vortex dynamo - Gissinger, Christophe

PHYSICS OF FLUIDS 26, (2014)

Abstract : 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. (C) 2014 AIP Publishing LLC.

PHYSICS OF FLUIDS 26, (2014)

LPS

Abstract : 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. (C) 2014 AIP Publishing LLC.

DOI

6

Dynamo efficiency controlled by hydrodynamic bistability - Miralles, Sophie and Herault, Johann and Fauve, Stephan and Gissinger, Christophe and Petrelis, Francois and Daviaud, Francois and Dubrulle, Berengere and Boisson, Jean and Bourgoin, Mickael and Verhille, Gautier and Odier, Philippe and Pinton, Jean-Francois and Plihon, Nicolas

PHYSICAL REVIEW E 89, (2014)

Abstract : Hydrodynamic and magnetic behaviors in a modified experimental setup of the von Karman sodium flow-where one disk has been replaced by a propeller-are investigated. When the rotation frequencies of the disk and the propeller are different, we show that the fully turbulent hydrodynamic flow undergoes a global bifurcation between two configurations. The bistability of these flow configurations is associated with the dynamics of the central shear layer. The bistable flows are shown to have different dynamo efficiencies; thus for a given rotation rate of the soft-iron disk, two distinct magnetic behaviors are observed depending on the flow configuration. The hydrodynamic transition controls the magnetic field behavior, and bifurcations between high and low magnetic field branches are investigated.

PHYSICAL REVIEW E 89, (2014)

LPS

Abstract : Hydrodynamic and magnetic behaviors in a modified experimental setup of the von Karman sodium flow-where one disk has been replaced by a propeller-are investigated. When the rotation frequencies of the disk and the propeller are different, we show that the fully turbulent hydrodynamic flow undergoes a global bifurcation between two configurations. The bistability of these flow configurations is associated with the dynamics of the central shear layer. The bistable flows are shown to have different dynamo efficiencies; thus for a given rotation rate of the soft-iron disk, two distinct magnetic behaviors are observed depending on the flow configuration. The hydrodynamic transition controls the magnetic field behavior, and bifurcations between high and low magnetic field branches are investigated.

DOI

7

Energy transfers during dynamo reversals - Mishra, Pankaj and Gissinger, Christophe and Dormy, Emmanuel and Fauve, Stephan

EPL 104, (2013)

Abstract : Using direct numerical simulations of the equations of magnetohydrodynamics, we study reversals of the magnetic field generated by the flow of an electrically conducting fluid in a sphere. We show that at low magnetic Prandtl numbers, Pm = 0.5, the decrease of magnetic energy, ohmic dissipation and power of the Lorentz force during a reversal is followed by an increase of the power injected by the force driving the flow and an increase of viscous dissipation. Cross correlations show that the power of the Lorentz force is in advance with respect to the other energy flows. We also observe that during a reversal, the maximum of the magnetic energy density migrates from one hemisphere to the other and comes back to its initial position, in agreement with recent experimental observations. For larger magnetic Prandtl numbers (Pm - 1, 2), the magnetic field reversals do not display these trends and strongly differ one from another. Copyright (C) EPLA, 2013

EPL 104, (2013)

LPS

Abstract : Using direct numerical simulations of the equations of magnetohydrodynamics, we study reversals of the magnetic field generated by the flow of an electrically conducting fluid in a sphere. We show that at low magnetic Prandtl numbers, Pm = 0.5, the decrease of magnetic energy, ohmic dissipation and power of the Lorentz force during a reversal is followed by an increase of the power injected by the force driving the flow and an increase of viscous dissipation. Cross correlations show that the power of the Lorentz force is in advance with respect to the other energy flows. We also observe that during a reversal, the maximum of the magnetic energy density migrates from one hemisphere to the other and comes back to its initial position, in agreement with recent experimental observations. For larger magnetic Prandtl numbers (Pm - 1, 2), the magnetic field reversals do not display these trends and strongly differ one from another. Copyright (C) EPLA, 2013

DOI

8

Morphology of field reversals in turbulent dynamos - Gissinger, C. and Dormy, E. and Fauve, S.

EPL 90, (2010)

Abstract : 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 P(m), i. e., the ratio between viscous and magnetic diffusivities. For P(m)similar to 1, the axial dipolar field reverses in the presence of a strong equatorial dipolar component, whereas for P(m) < 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 P(m). Copyright (C) EPLA, 2010

EPL 90, (2010)

LPS

Abstract : 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 P(m), i. e., the ratio between viscous and magnetic diffusivities. For P(m)similar to 1, the axial dipolar field reverses in the presence of a strong equatorial dipolar component, whereas for P(m) < 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 P(m). Copyright (C) EPLA, 2010

DOI

9

Dynamo regimes and transitions in the VKS experiment - Berhanu, M. and Verhille, G. and Boisson, J. and Gallet, B. and Gissinger, C. and Fauve, S. and Mordant, N. and Petrelis, F. and Bourgoin, M. and Odier, P. and Pinton, J. -F. and Plihon, N. and Aumaitre, S. and Chiffaudel, A. and Daviaud, F. and Dubrulle, B. and Pirat, C.

EUROPEAN PHYSICAL JOURNAL B 77, 459-468 (2010)

Abstract : The Von Karman Sodium experiment yields a variety of dynamo regimes, when asymmetry is imparted to the flow by rotating impellers at different speed F (1) and F (2). We show that as the intensity of forcing, measured as F (1)+F (2), 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 theta = (F (1)-F (2))/(F (1)+F (2)), 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.

EUROPEAN PHYSICAL JOURNAL B 77, 459-468 (2010)

LPS

Abstract : The Von Karman Sodium experiment yields a variety of dynamo regimes, when asymmetry is imparted to the flow by rotating impellers at different speed F (1) and F (2). We show that as the intensity of forcing, measured as F (1)+F (2), 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 theta = (F (1)-F (2))/(F (1)+F (2)), 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.

DOI

10

Direct numerical simulations of the galactic dynamo in the kinematic growing phase - Gissinger, Christophe and Fromang, Sebastien and Dormy, Emmanuel

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 394, L84-L88 (2009)

Abstract : We present kinematic simulations of a galactic dynamo model based on the large-scale differential rotation and the small-scale helical fluctuations due to supernova explosions. We report for the first time direct numerical simulations of the full galactic dynamo using an un-parametrized global approach. We argue that the scale of helicity injection is large enough to be directly resolved rather than parametrized. While the actual superbubble characteristics can only be approached, we show that numerical simulations yield magnetic structures which are close to both the observations and the previous parametrized mean field models. In particular, the quadrupolar symmetry and the spiraling properties of the field are reproduced. Moreover, our simulations show that the presence of a vertical inflow plays an essential role to increase the magnetic growth rate. This observation could indicate an important role of the downward flow (possibly linked with galactic fountains) in sustaining galactic magnetic fields.

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 394, L84-L88 (2009)

LPS

Abstract : We present kinematic simulations of a galactic dynamo model based on the large-scale differential rotation and the small-scale helical fluctuations due to supernova explosions. We report for the first time direct numerical simulations of the full galactic dynamo using an un-parametrized global approach. We argue that the scale of helicity injection is large enough to be directly resolved rather than parametrized. While the actual superbubble characteristics can only be approached, we show that numerical simulations yield magnetic structures which are close to both the observations and the previous parametrized mean field models. In particular, the quadrupolar symmetry and the spiraling properties of the field are reproduced. Moreover, our simulations show that the presence of a vertical inflow plays an essential role to increase the magnetic growth rate. This observation could indicate an important role of the downward flow (possibly linked with galactic fountains) in sustaining galactic magnetic fields.

DOI

11

A numerical model of the VKS experiment - Gissinger, C. J. P.

EPL 87, (2009)

Abstract : 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. Copyright (C) EPLA, 2009

EPL 87, (2009)

LPS

Abstract : 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. Copyright (C) EPLA, 2009

DOI

12

Effect of magnetic boundary conditions on the dynamo threshold of von Karman swirling flows - Gissinger, C. and Iskakov, A. and Fauve, S. and Dormy, E.

EPL 82, (2008)

Abstract : 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. Copyright (c) EPLA, 2008.

EPL 82, (2008)

LPS

Abstract : 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. Copyright (c) EPLA, 2008.

DOI

13

Bypassing Cowling's theorem in axisymmetric fluid dynamos - Gissinger, Christophe and Dormy, Emmanuel and Fauve, Stephan

PHYSICAL REVIEW LETTERS 101, (2008)

Abstract : 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.

PHYSICAL REVIEW LETTERS 101, (2008)

LPS

Abstract : 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.