H. Kitauchi

S. Kida

National Institute for Fusion Science (NIFS-Repository)

§14. Generation of Magnetic Field in Thermal Convection in a Rotating Spherical Shell Kida, S. Kitauchi, H. (RIMS, Kyoto U.) In order to obtain a hint of possible scenario of generation and maintenance of geomagnetic field we make a direct numerical simulation of a system of MHD equations and a detailed anal-ysis of the numerical data. The molten iron in the outer core of the Earth is modelled by an electrically conducting Boussinesq fluid con-tained in a spherical shell sandwiched by two concentric spheres which rotate around a com-mon axis with a constant common angular ve-locity n. The inner boundry is hotter than the outer. There are four dimensionless parameters which control this dynamical system, that is, the Prandtl number Pr = v / K, the Rayleigh number Ra = a1~Td4 / KV, the Taylor number Ta = (2lnld2 jv) 2 , the magnetic Prantl number Pm =A./ K, and the radius ratio rJ of the two spherical boundaries. Here, v is the kinematic viscosity of fluid, K the thermal diffusivity, a the thermal expan-sion coefficient, 1 a gravity constant, ~T the temperature difference between the two bound-aries, d the shell thickness, and A the electrical resistivity. The simulation is performed in two steps. First, a steady thermal convection velocity field without magnetic field is realized starting with a stationary thermal conduction state super-imposed by random perturbations in the ve-locity field. The values of parameters chosen are Ra = 3200, Ta = 8000, Pr = 1, and 7] = 0.5, for which the initial thermal conduction 264 state is slightly unstable to small perturbations. Five pairs of cyclonic and anti-cyclonic vortex columns, which arrange alternately, are realized in the steady state (see Fig.l). Then, a small random magnetic field is seeded in the steady state and the full MHD equations are solved numerically. For Pm = 0.12 a time-dependent weak magnetic field is generated which drifts eastward relative to the vortex columns and changes periodically in time. The regions of strong magnetic field are con-fined in some restricted domains of peculiar shape In Fig.l we show the spatial structure of the velocity and magnetic fields around the cen-tral axis of an anti-cyclonic vortex which is one of the regions of strong magnetic field. Here, the blue lines represent the magnetic flux lines, the red/white lines the streamlines. The mag-netic field is generated on red regions. The flow spirals clockwise into the anti-cyclonic vor-tex while going away from the equatorial plane. The transparent and yellow iso-surfaces cover high-vorticity and high-magnetic fields regions, respectively. Fig.l. Intensification of magnetic field by concentrate-and-stretch mechanism. 

Generation of Magnetic Field in Thermal Convection in a Rotating Spherical Shell

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