Magnetic induction and diffusion mechanisms in a liquid sodium spherical Couette experiment

Cabanes, Simon; Schaeffer, Nathanaël; Nataf, Henri-Claude

doi:10.1103/physreve.90.043018

Cited by 9 publications

(18 citation statements)

References 29 publications

(75 reference statements)

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“…Indeed, the authors speculate that if the magnitude of this negative β effect were to grow large enough, it could promote dynamo action. As reported in another paper (Cabanes et al 2014), the ω effect is present in the rotationally dominated outer region, which is another possible ingredient of dynamo action.…”

Section: The Derviche Tourneur Sodium Experiment: the Magnetostrophicmentioning

confidence: 67%

Liquid sodium models of the Earth’s core

Adams

Stone

Zimmerman

et al. 2015

Prog. in Earth and Planet. Sci.

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Our understanding of the dynamics of the Earth's core can be advanced by a combination of observation, experiments, and simulations. A crucial aspect of the core is the interplay between the flow of the conducting liquid and the magnetic field this flow sustains via dynamo action. This non-linear interaction, and the presence of turbulence in the flow, precludes direct numerical simulation of the system with realistic turbulence. Thus, in addition to simulations and observations (both seismological and geomagnetic), experiments can contribute insight into the core dynamics. Liquid sodium laboratory experiments can serve as models of the Earth's core with the key ingredients of conducting fluid, turbulent flow, and overall rotation, and can also approximate the geometry of the core. By accessing regions of parameter space inaccessible to numerical studies, experiments can benchmark simulations and reveal phenomena relevant to the Earth's core and other planetary cores. This review focuses on the particular contribution of liquid sodium spherical Couette devices to this subject matter.

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Section: The Derviche Tourneur Sodium Experiment: the Magnetostrophicmentioning

confidence: 67%

Liquid sodium models of the Earth’s core

Adams

Stone

Zimmerman

et al. 2015

Prog. in Earth and Planet. Sci.

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“…The code uses second order finite differences in the radial direction with many points concentrated near the walls (boundary layers) and the spherical harmonic transform library SHTns (Schaeffer 2013) in the latitudinal direction, as well as hybrid parallel execution using OpenMP and/or MPI. XSHELLS v1.4 uses a semi-implicit time-stepping scheme with diffusive terms treated by the Crank-Nicolson (Figueroa et al 2013;Cabanes et al 2014a), the DTS-Ω experiment (Kaplan et al 2018), as well as unmagnetized spherical Couette (Barik et al 2018) and torsional Alfvén waves (Gillet et al 2012;Schaeffer et al 2012;Schaeffer and Jault 2016).…”

Section: Numerical Set-upmentioning

confidence: 99%

“…The magnetic boundary conditions require a special treatment because of the electric conductivity jumps between the inner sphere, the liquid, and the outer shell, which we keep the same as in the DTS-Ω experiment, given in Table 2. The procedure is described in detail in Appendix C of Cabanes et al (2014a).…”

Section: Numerical Set-upmentioning

confidence: 99%

Torsional Alfvén waves in a dipolar magnetic field: experiments and simulations

Tigrine

Nataf

Schaeffer

et al. 2019

Geophysical Journal International

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SUMMARY The discovery of torsional Alfvén waves (geostrophic Alfvén waves) in the Earth’s core (Gillet et al. 2010) calls for a better understanding of their properties. We present the first experimental observations of torsional Alfvén waves, performed in the DTS-Ω set-up. In this set-up, 50 L of liquid sodium are confined between an inner sphere (ri = 74 mm) and an outer shell (ro = 210 mm). The inner sphere houses a permanent magnet, imposing a dipolar magnetic field (Bmax = 345 mT). Both the inner sphere and the outer shell can rotate around the vertical axis. Alfvén waves are triggered by a sudden jerk of the inner sphere. We study the propagation of these waves when the fluid is initially at rest, and when it spins at a rotation rate up to 15 Hz. We measure the azimuthal magnetic field of the wave at different radii inside the fluid with magnetometers installed in a sleeve. We also record the electric potential signature on the outer shell at several latitudes. Besides, we probe the associated azimuthal velocity field using ultrasound Doppler velocimetry. With a 15 Hz rotation rate, the dynamical regimes we achieve are characterized by dimensionless numbers in the following ranges: Lundquist number 0.5 < Lu < 12, Lehnert number 0.01 < Le < 0.26, Rossby number Ro ∼ 0.1. We observe that the magnetic signal propagates away from the inner sphere, strongly damped by magnetic diffusion. Rotation affects the magnetic signature in a subtle way. Its effect is more pronounced on the surface electric potentials, which are sensitive to the actual fluid velocity of the wave. The ultrasound Doppler probes provide the first experimental measurement of the fluid velocity of an Alfvén wave. To complement these observations, we ran numerical simulations, using the XSHELLS pseudospectral code with parameters as close as possible to the experimental ones. The synthetic magnetic and electric signals match our measurements. The meridional snapshots of the synthetic azimuthal velocity field reveal the formation of geostrophic cylinders expected for torsional Alfvén waves. We establish scaling laws for the magnetic and kinetic energies of Alfvén waves with and without rotation. In both cases, we find that the magnetic energy EM saturates at a level proportional to $Rm_{\rm jerk}^2$, where Rmjerk = Ujerkro/η is the magnetic Reynolds number built with the maximum azimuthal velocity of the inner sphere during the jerk. The $E_K^{\rm max}/E_M^{\rm max}$ ratio (where $E_K^{\rm max}$ is the maximum kinetic energy), close to 1 for very quick jerks, increases linearly with the jerk duration.

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“…Everything stays spherically symmetric to fit in a spectral framework. However, as the goal is to investigate the properties of a real experiment, the applied magnetic field is chosen to approximate the field of DTS-Ω's inner magnet, rather than a pure dipole, including magnetic harmonics up to degree 11 and order 6 [19].…”

Section: Numerical Modelmentioning

confidence: 99%

Dynamic domains of the Derviche Tourneur sodium experiment: Simulations of a spherical magnetized Couette flow

2018

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The Derviche Tourneur Sodium experiment, a spherical Couette magnetohydrodynamics experiment with liquid sodium as the medium and a dipole magnetic field imposed from the inner sphere, recently underwent upgrades to its diagnostics to better characterize the flow and induced magnetic fields with global rotation. In tandem with the upgrades, a set of direct numerical simulations were run to give a more complete view of the fluid and magnetic dynamics at various rotation rates of the inner and outer spheres. These simulations reveal several dynamic regimes, determined by the Rossby number. At positive differential rotation there is a regime of quasigeostrophic flow, with low levels of fluctuations near the outer sphere. Negative differential rotation shows a regime of what appear to be saturated hydrodynamic instabilities at low negative differential rotation, followed by a regime where filamentary structures develop at low latitudes and persist over five to ten differential rotation periods as they drift poleward. We emphasize that all these coherent structures emerge from turbulent flows. At least some of them seem to be related to linear instabilities of the mean flow. The simulated flows can produce the same measurements as those that the physical experiment can take, with signatures akin to those found in the experiment. This paper discusses the relation between the internal velocity structures of the flow and their magnetic signatures at the surface.Typeset by REVT E X arXiv:1610.03964v4 [physics.flu-dyn]

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Magnetic induction and diffusion mechanisms in a liquid sodium spherical Couette experiment

Cited by 9 publications

References 29 publications

Liquid sodium models of the Earth’s core

Liquid sodium models of the Earth’s core

Torsional Alfvén waves in a dipolar magnetic field: experiments and simulations

Dynamic domains of the Derviche Tourneur sodium experiment: Simulations of a spherical magnetized Couette flow

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