Magnetic induction maps in a magnetized spherical Couette flow experiment

Nataf, Henri-Claude

doi:10.1016/j.crhy.2012.12.002

Cited by 12 publications

(29 citation statements)

References 42 publications

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“…Following earlier works [8,10], we collect ultrasound Doppler velocity profiles, electric potential measurements, global torque data, and measurements of the induced magnetic field inside the sodium layer, to reconstruct meridional maps of the mean flow and magnetic field at a given Rm, taking into account the link established by the induction equation. But we further constrain these fields by analyzing the response of the fluid shell to a time-periodic magnetic field, as in Frick et al [4].…”

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Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment

2014

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The contribution of small scale turbulent fluctuations to the induction of mean magnetic field is investigated in our liquid sodium spherical Couette experiment with an imposed magnetic field. An inversion technique is applied to a large number of measurements at Rm ≈ 100 to obtain radial profiles of the α and β effects and maps of the mean flow. It appears that the small scale turbulent fluctuations can be modeled as a strong contribution to the magnetic diffusivity that is negative in the interior region and positive close to the outer shell. Direct numerical simulations of our experiment support these results. The lowering of the effective magnetic diffusivity by small scale fluctuations implies that turbulence can actually help to achieve self-generation of large scale magnetic fields.The Earth, the Sun and many other astrophysical bodies produce their own magnetic field by dynamo action, where the induction of a magnetic field by fluid motion overcomes the Joule dissipation. In all astrophysical bodies, the conducting fluid undergoes turbulent motions, which can also significantly affect the induction of a largescale magnetic field by either enhancing it or weakening it. It is therefore of primary interest to quantify the role of these fluctuations in the dynamo problem.The induction equation for the mean magnetic field B reads:where U is the mean velocity field, η = (µ 0 σ) −1 is the magnetic diffusivity (involving the magnetic permeability µ 0 and the conductivity of the fluid σ), and E = ũ ×b is the mean electromotive force (emf) due to small scale fluctuating magneticb and velocityũ fields. The relative strength between the inductive and dissipative effects is given by the magnetic Reynolds number Rm = U L/η (U and L are characteristic velocity and the characteristic length-scale). When there is a scale separation between the turbulent fluctuations and the mean flow, we can follow the mean-field theory and expand the emf in terms of mean magnetic quantities: E = α B − β∇ × B . For homogeneous isotropic turbulence, α and β are scalar quantities. α is related to the flow helicity and results in an electrical current aligned with the mean magnetic field, whereas β can be interpreted as a turbulent diffusivity effectively increasing (β > 0) or decreasing (β < 0) electrical currents. The effective magnetic diffusivity η ef f = η + β can have tremendous effects on energy dissipation and on dynamo action by reducing or increasing the effective magnetic Reynolds number Rm ef f = U L/η ef f .However, direct determination of these small-scale contributions remains a challenging issue for experimental studies and numerical simulations.The first generation of dynamo experiments were designed to show that turbulent flows with strong geometrically-imposed helicity could self-generate their own magnetic fields. Since the success of Riga [1] and Karlsruhe [2] dynamos, several other liquid metal experiments have sought to overcome the effects of magnetohydrodynamic turbulence in less constrained, more geophysically rele...

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Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment

2014

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“…The m = 0 data and data errors are acquired and processed as described by Nataf [21]. The main difference is that we focus here on data for a rotation rate f = ±9 Hz, instead of ±3 Hz in [21].…”

Section: Axisymmetric Data Acquisition and Processingmentioning

confidence: 99%

“…In an effort to evaluate the contributions of turbulent fluctuations to the mean large-scale magnetic field in the DTS experiment, Nataf [21] inverted simultaneously mean velocity and magnetic data in order to evaluate by difference the part of the mean magnetic field that is not induced by the mean velocity field. He also evaluated an upper bound for the contribution of the fluctuations to the mean field by mapping the amplitude of magnetic and velocity fluctuations.…”

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confidence: 99%

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

2014

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We present a reconstruction of the mean axisymmetric azimuthal and meridional flows in the DTS liquid sodium experiment. The experimental device sets a spherical Couette flow enclosed between two concentric spherical shells where the inner sphere holds a strong dipolar magnet, which acts as a magnetic propeller when rotated. Measurements of the mean velocity, mean induced magnetic field and mean electric potentials have been acquired inside and outside the fluid for an inner sphere rotation rate of 9 Hz (Rm 28). Using the induction equation to relate all measured quantities to the mean flow, we develop a nonlinear least square inversion procedure to reconstruct a fully coherent solution of the mean velocity field. We also include in our inversion the response of the fluid layer to the non-axisymmetric time-dependent magnetic field that results from deviations of the imposed magnetic field from an axial dipole. The mean azimuthal velocity field we obtain shows super-rotation in an inner region close to the inner sphere where the Lorentz force dominates, which contrasts with an outer geostrophic region governed by the Coriolis force, but where the magnetic torque remains the driver. The meridional circulation is strongly hindered by the presence of both the Lorentz and the Coriolis forces. Nevertheless, it contributes to a significant part of the induced magnetic energy. Our approach sets the scene for evaluating the contribution of velocity and magnetic fluctuations to the mean magnetic field, a key question for dynamo mechanisms.

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“…However, for our current problem, a more simple and lighter method makes use of the fact that the spherical harmonics form a natural basis for both the acoustic modes and the flow field. More specifically, the azimuthal velocity field θ Ω θ θ = ϕ U r r r ( , ) ( , ) sin can be written as [12]:…”

Section: Semi-spectral Bayesian Inversionmentioning

confidence: 99%

Helioseismology in a bottle: modal acoustic velocimetry

et al. 2014

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Measurement of the differential rotation of the Sunʼs interior is one of the great achievements of helioseismology, providing important constraints for stellar physics. The technique relies on observing and analyzing rotationally-induced splittings of p-modes in the star. Here, we demonstrate the first use of the technique in a laboratory setting. We apply it in a spherical cavity with a spinning central core (spherical-Couette flow) to determine the mean azimuthal velocity of the air filling the cavity. We excite a number of acoustic resonances (analogous to p-modes in the Sun) using a speaker and record the response with an array of small microphones on the outer sphere. Many observed acoustic modes show rotationally-induced splittings, which allow us to perform an inversion to determine the airʼs azimuthal velocity as a function of both radius and latitude. We validate the method by comparing the velocity field obtained through inversion against the velocity profile measured with a calibrated hot film anemometer. This modal acoustic velocimetry technique has great potential for laboratory setups involving rotating fluids in axisymmetric cavities. It will be useful especially in liquid metals where direct optical methods are unsuitable and ultrasonic techniques very challenging at best.

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Magnetic induction maps in a magnetized spherical Couette flow experiment

Cited by 12 publications

References 42 publications

Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment

Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment

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

Helioseismology in a bottle: modal acoustic velocimetry

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