Numerical Simulation of a Turbulent Magnetic Dynamo

Abstract

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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