Mathematics – Dynamical Systems
Scientific paper
May 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996aas...188.6901r&link_type=abstract
American Astronomical Society, 188th AAS Meeting, #69.01; Bulletin of the American Astronomical Society, Vol. 28, p.935
Mathematics
Dynamical Systems
Scientific paper
In the usual alpha omega dynamo, runaway growth of the magnetic field is prevented by introducing arbitrary quenching factors. These roughly represent the back-reaction of the magnetic field on the flow by multiplying alpha and omega by some decreasing function of the mean toroidal magnetic field strength. This approach, while straightforward, has only limited physical justification. Here we take an alternate approach by allowing alpha or omega to vary with latitude and time and derive dynamical equations for them using principles of energy conservation. The resulting system of nonlinear partial differential equations is approximated by a truncated Fourier-Galerkin expansion, leading to a system of nonlinear ordinary differential equations whose behavior is studied using the methods of nonlinear dynamical systems. The results show that low-order truncations of the system give misleading results, but at higher orders the system converges to give consistent behavior, independent of truncation order. Somewhat surprisingly, the results depend strongly on which effect we choose to make dynamically variable. The back-reaction on omega appears to be far more important in reproducing Sun-like dynamo oscillations.
Roald Colin B.
Thomas John H.
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