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Modelling the solar dynamo using the Lorenz equations
Derivation
We can obtain the Lorenz equations by truncating the mean field dynamo equations to the minimum number of terms. Details can be found, for example, in
- Martens P.C.H., 1984, Physical Reports, vol 115, pp 315-378
- Covas E., Tworkowski A., Brandenburg A., Tavakol A., 1997, Astron. Astrophys. 317, 610-617
- Priest E., 1982, Solar Magnetohydrodynamics (chapter 9, 340-341) D. Reidel Publishing company
The equations are
Here
- τp is the diffusion time for the poloidal field
- τφ is the diffusion time for the toroidal field
- τα is the adjustment timescale accounting for the reduation in α due to the Lorenz force and the finite time needed for this adjustment
- ω is the rotation frequency of the Sun
- L is the depth of the convection zone, and
- b is non-dimensional dynamo number.
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