<i>Colloquium</i>: Laboratory experiments on hydromagnetic dynamos

Gailitis, A.; Lielausis, O.; Platacis, E.; Gerbeth, Günter; Stefani, Frank

doi:10.1103/revmodphys.74.973

Cited by 106 publications

(103 citation statements)

References 94 publications

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“…104501-2 flow) it was proved that the vertical magnetic field condition ( [6,26]) provided reasonable predictions of the theoretically estimated (based on the convective instabilities of the Ponomarenko dynamo, [4,6] …”

Section: 104501 (2007) P H Y S I C a L R E V I E W L E T T E R S mentioning

confidence: 99%

Numerical Simulation of a Turbulent Magnetic Dynamo

Kenjereš

Hanjalić

2007

Phys. Rev. Lett.

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We present numerical simulations of a turbulent magnetic dynamo mimicking closely the Riga-dynamo experiment at Re 3:5 10 6 and 15 Re m 20. The Reynolds-averaged Navier-Stokes equations for the fluid flow and turbulence field are solved simultaneously with the direct numerical solution of the magnetic field equations. The fully integrated two-way-coupled simulations reproduced all features of the magnetic self-excitation detected by the Riga experiment, with frequencies and amplitudes of the selfgenerated magnetic field in good agreement with the experimental records, and provided full insight into the unsteady magnetic and velocity fields and the mechanisms of the dynamo action. DOI: 10.1103/PhysRevLett.98.104501 PACS numbers: 47.11.ÿj, 47.27.Eÿ, 47.65.ÿd, 91.25.Cw Complex interactions between turbulent flow of electrically conductive fluids and electromagnetic fields play the key role in many physical phenomena in nature and technology. Of particular interest is the conversion of the mechanical energy of a moving electrically conductive medium into the magnetic energy, known as the magnetic dynamo. It is believed that the magnetic dynamo effects are responsible for the creation of magnetic fields in spiral galaxies, stars, and planets (including Earth's magnetic field), e.g., [1]. In order to create the favorable conditions for possible self-excitation of a magnetic field, it is necessary to achieve regimes where stretching of the magnetic field will overcome its resistive damping. This condition is defined by the critical magnetic Reynolds number Re m UL= > 1 (where U and L are typical velocity and length scale, respectively, and is magnetic diffusivity). In order to reach such conditions, one needs relatively large length scales and high velocities -even for the best electrically conductive fluids (e.g., liquid sodium, 1= 0 0:1 m 2 =s), where 0 and are the magnetic permeability and electric conductivity. For such configurations, the hydrodynamical Reynolds number (Re UL= ) will be also very high (Re 10 5 -10 6 ), making the flow highly turbulent. Experimental studies of magnetic fluid dynamos face many practical problems associated with large dimensions of setups and potentially hazardous working fluids (sodium). This explains why it was not until late 1999 when two experimental groups in Riga ([2 -6]) and Karlsruhe ([7-9]) finally and independently succeeded in detecting the self-excitation and subsequent sustenance of a magnetic field for the very first time. Although this is an important step towards understanding and explaining the Earth's magnetic field from the magnetic dynamo effect, both experiments were not designed to actually mimic the Geo-Dynamo (Earth-like) conditions, but rather to provide experimental proof of the magnetic field self-amplification.Despite their remarkable success, the experimental studies provided only the time records of the magnetic field components at particular locations -so information addressing the detailed spatial distribution of the magnetic field and its dynamics...

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Section: 104501 (2007) P H Y S I C a L R E V I E W L E T T E R S mentioning

confidence: 99%

Numerical Simulation of a Turbulent Magnetic Dynamo

Kenjereš

Hanjalić

2007

Phys. Rev. Lett.

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“…5,6 Since then, a number of experiments have been carried out at both places providing a wealth of data on the dynamo behavior in the kinematic and the saturation regime. [7][8][9][10][11][12][13][14][15][16][17][18] Further dynamorelated experiments are being prepared or carried out at various places in the world. [19][20][21][22][23] Although, up to present, they have not yet reached the self-excitation condition, they have brought about many interesting results, in particular concerning the role of turbulence in flows with large Re m .…”

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confidence: 99%

Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

et al. 2006

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Magnetic fields of planets, stars, and galaxies result from self-excitation in moving electroconducting fluids, also known as the dynamo effect. This phenomenon was recently experimentally confirmed in the Riga dynamo experiment ͓A. Gailitis et al., Phys. Rev. Lett. 84, 4365 ͑2000͒; A. Gailitis et al., Physics of Plasmas 11, 2838 ͑2004͔͒, consisting of a helical motion of sodium in a long pipe followed by a straight backflow in a surrounding annular passage, which provided adequate conditions for magnetic-field self-excitation. In this paper, a first attempt to simulate computationally the Riga experiment is reported. The velocity and turbulence fields are modeled by a finite-volume Navier-Stokes solver using a Reynolds-averaged-Navier-Stokes turbulence model. The magnetic field is computed by an Adams-Bashforth finite-difference solver. The coupling of the two computational codes, although performed sequentially, provides an improved understanding of the interaction between the fluid velocity and magnetic fields in the saturation regime of the Riga dynamo experiment under realistic working conditions.

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“…Determining the onset conditions for magnetic field growth in magnetohydrodynamics is fundamental to understanding how astrophysical dynamos such as the Earth, the Sun, and the galaxy self-generate magnetic fields. These onset conditions are now being studied in laboratory experiments using flows of liquid sodium [1]. The conditions required for generating a dynamo can be determined by solving the magnetic induction equation…”

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confidence: 99%

“…These onset conditions are now being studied in laboratory experiments using flows of liquid sodium [1]. The conditions required for generating a dynamo can be determined by solving the magnetic induction equation…”

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confidence: 99%

Intermittent Magnetic Field Excitation by a Turbulent Flow of Liquid Sodium

et al. 2006

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The magnetic field measured in the Madison Dynamo Experiment shows intermittent periods of growth when an axial magnetic field is applied. The geometry of the intermittent field is consistent with the fastest growing magnetic eigenmode predicted by kinematic dynamo theory using a laminar model of the mean flow. Though the eigenmodes of the mean flow are decaying, it is postulated that turbulent fluctuations of the velocity field change the flow geometry such that the eigenmode growth rate is temporarily positive. Therefore, it is expected that a characteristic of the onset of a turbulent dynamo is magnetic intermittency. Determining the onset conditions for magnetic field growth in magnetohydrodynamics is fundamental to understanding how astrophysical dynamos such as the Earth, the Sun, and the galaxy self-generate magnetic fields. These onset conditions are now being studied in laboratory experiments using flows of liquid sodium [1]. The conditions required for generating a dynamo can be determined by solving the magnetic induction equationwhere B is the magnetic field, V is the velocity field scaled by a characteristic speed V 0 , and the time is scaled to the resistive diffusion time τ σ = µ 0 σL 2 . The magnetic Reynolds number is Rm = µ 0 σLV 0 , where σ is the conductivity of the fluid and L is a characteristic scale length [2]. In the kinematic approximation, the velocity field is assumed to be a prescribed flow (either the flow is stationary or its time dependence is specified) and Lorentz forces due to the magnetic field are neglected. Equation 1 is then linear in B and can be solved as an eigenvalue problem. Several different types of stationary, helical flows have been shown theoretically to be kinematic dynamos [3,4,5,6], which in turn has lead to the design of current dynamo experiments. For particular flows, the kinematic model predicts a critical value of the magnetic Reynolds number, Rm crit , above which the magnetic field becomes linearly unstable, i.e. for Rm > Rm crit a small seed magnetic field will grow exponentially in time. The dynamo onset conditions have been tested in helical pipe-flow experiments at Riga [7,8] and Karlsruhe [9,10]. Both experiments generated magnetic fields at a value of Rm crit consistent with predictions from the kinematic theory.Fluids and plasmas such as the Earth's liquid core, the solar convection zone, and liquid metals are turbulent under the conditions required for a dynamo. The

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Colloquium: Laboratory experiments on hydromagnetic dynamos

Cited by 106 publications

References 94 publications

Numerical Simulation of a Turbulent Magnetic Dynamo

Numerical Simulation of a Turbulent Magnetic Dynamo

Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

Intermittent Magnetic Field Excitation by a Turbulent Flow of Liquid Sodium

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