Physics – Fluid Dynamics
Scientific paper
Dec 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982gapfd..22..235f&link_type=abstract
Geophysical and Astrophysical Fluid Dynamics, vol. 22, no. 3-4, 1982, p. 235-279.
Physics
Fluid Dynamics
21
Convection, Dynamo Theory, Geomagnetism, Magnetic Field Configurations, Magnetohydrodynamic Stability, Approximation, Astronomical Models, Differential Equations, Hartmann Number, Magnetic Diffusion, Plane Waves, Taylor Instability
Scientific paper
The weak-field Bernard-type dynamo considered by Soward (1974) is treated here at higher levels of the induced magnetic field. It is found that two sources of instability occur in the intermediate field regime where M is approximately equal to T to the 1/12th, M and T being, respectively, the Hartmann and Taylor numbers. On the time scale of magnetic diffusion, solutions may blow up in finite time as a result of destabilization of the convection by the magnetic field. On a faster time scale, a dynamic instability related to MAC-wave instability can also take place. It is concluded therefore that the asymptotic structure of this dynamo is unstable to virtual increases in the magnetic field energy. In an endeavor to model stabilization of the dynamo in a strong-field regime, two approximations are considered. In the first, a truncated expansion in three-dimensional plane waves is investigated numerically. A second approach makes use of an ad hoc set of ordinary differential equations containing many of the features of convection dynamos at all field energies.
Childress Stephen
Fautrelle Yves
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