Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment

Abstract

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...

Rotating convective turbulence in Earth and planetary cores

“…Given accurate field models, it is essential to generate advanced models of the essential turbulent processes and dynamo physics occurring in liquid metals. Efforts are being made in this direction via laboratory experiments (e.g., Cabanes et al, 2014;Zimmerman et al, 2014;Ribeiro et al, 2015). To computationally access turbulent liquid metal dynamo action, numerical models will need to be run on tens to hundreds of thousands of cores.…”

Liquid sodium models of the Earth’s core

“…An experimental observation of the β effect was first reported in Reighard and Brown (2001), with the turbulence leading to an increase in the effective resistivity of the fluid. As noted above, both positive and negative β effects have been seen in some of the experiments described above (Cabanes et al 2014a;Nornberg et al 2006). The influence of turbulence is thus variable.…”

“…Cabanes et al (2014a) report on measurements of the α and β effects and note that the β effect due to small-scale turbulent fluctuations is negative in the interior of the experiment and positive closer to the outer sphere. Thus, the turbulent fluctuations near the inner sphere reduce the effective magnetic diffusivity, implying that turbulence could be a contributing factor to dynamo action, as opposed to a hindrance (as it has often seemed in past experiments).…”

Fluid Dynamics of Earth’s Core: Geodynamo, Inner Core Dynamics, Core Formation

“…Though numerical dynamo calculations are now well established, liquid metal experiments are still very valuable tools for understanding planetary core dynamics (e.g. Nataf and Gagnière, 2008;Cabanes et al, 2014). On certain aspects liquid metal experiments are dynamically closer to Earth's core conditions than numerical simulations.…”