Linear astrophysical dynamos in rotating spheres - Mode transition between steady and oscillatory dynamos as a function of dynamo strength and anisotropic turbulent magnetic diffusivity

Details Linear astrophysical dynamos in rotating spheres - Mode transition between steady and oscillatory dynamos as a function of dynamo strength and anisotropic turbulent magnetic diffusivity Linear astrophysical dynamos in rotating spheres - Mode transition between steady and oscillatory dynamos as a function of dynamo strength and anisotropic turbulent magnetic diffusivity

Aug 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984apj...283..870y&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 283, Aug. 15, 1984, p. 870-878.

Astronomy and Astrophysics

Astrophysics

11

Dynamo Theory, Magnetohydrodynamic Turbulence, Solar Magnetic Field, Solar Oscillations, Solar Rotation, Astronomical Models, Geomagnetism, Magnetic Diffusion, Magnetic Variations, Magnetohydrodynamic Waves, Rotating Spheres, Solar Cycles

Scientific paper

Linear solutions of the dynamo equation with anisotropic diffusivity in a spherical shell are investigated for a wide range of dynamo numbers as a basis for understanding the behavior of nonlinear dynamos with variable dynamo strength as a function of magnetic field. The dynamo equation has growing oscillatory solutions for high dynamo numbers, or equivalently for small magnetic diffusivity. Solutions for intermediate dynamo number can be oscillatory with negative growth rates or steady with positive growth rates, depending on structure of differential rotation and anisotropic diffusivity. For low dynamo numbers, both oscillatory and steady solutions have negative growth rates. For extremely low dynamo numbers, only steady modes with large negative growth rates prevail. Odd-even parity selection rules for steady modes are opposite to those for oscillatory modes: Odd (even) parity is selected for steady modes when dynamo waves that are potential solutions of the same dynamo system with smaller growth rates propagate away from (toward) the equator with differential rotation decreasing (increasing) inward. Effects of anisotropic diffusivity for steady modes depend on differential rotation. For poleward increasing latitudinal-gradient-dominated differential rotation, which easily gives rise to growing steady modes, smaller diffusivity in the radial direction than in the latitudinal direction separates odd and even modes better but suppresses growth rates of the steady modes. For equatorward increasing latitudinal-gradient-dominated differential rotation, growing steady modes are difficult to be achieved. For radial-gradient-dominated differential rotation, larger diffusivity in the radial direction suppresses the growth rates. Implication of the results for understanding solar cycle multiple period nonlinear oscillations with Maunder-minimum-like era and sporadic polarity transitions of the Earth's almost steady magnetic fields through temporary oscillatory phases is discussed.

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