Magnetic field generation by convective flows in a plane layer |
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Authors: | O M Podvigina |
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Institution: | 1. International Institute of Earthquake Prediction Theory and Mathematical Geophysics, 79 bldg.?2, Warshavskoe ave., 117556, Moscow, Russian Federation 2. Laboratory of General Aerodynamics, Institute of Mechanics, Lomonosov Moscow State University, 1, Michurinsky ave., 119899, Moscow, Russian Federation 3. Observatoire de la C?te d'Azur, BP?4229, 06304, Nice Cedex 4, France
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Abstract: | Hydrodynamic and magnetohydrodynamic convective attractors in a plane
horizontal layer 0≤z≤1 are investigated numerically.
We consider Rayleigh-Bénard convection in Boussinesq approximation assuming
stress-free boundary conditions on horizontal
boundaries and periodicity with the same period L in the x and y
directions. Computations have been performed for the Prandtl number P=1
for
and Rayleigh numbers 0<R≤4000, and for L=4, 0<R≤2000.
Fifteen different types of hydrodynamic attractors are found, including two
types of steady
states distinct from rolls, travelling waves, periodic and quasiperiodic flows,
and chaotic attractors of heteroclinic nature. Kinematic dynamo problem has been
solved for the computed convective attractors. Out of the 15 types of
the observed attractors only 6 can act as kinematic dynamos. Nonlinear
magnetohydrodynamic regimes have been explored assuming as initial conditions
convective attractors capable of magnetic field generation, and a small seed
magnetic field. After initial exponential growth, in the saturated regime
magnetic energy remains much smaller than the flow kinetic energy.
The final magnetohydrodynamic attractors are either quasiperiodic or chaotic. |
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Keywords: | 47 20 Ky Nonlinearity bifurcation and symmetry breaking 47 20 Bp Buoyancy-driven instabilities (e g Rayleigh-Benard) 91 25 Cw Origins and models of the magnetic field dynamo theories |
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