1. Cellular Dynamo in a Rotating Spherical Shell Alexander Getling Lomonosov Moscow State University Moscow, Russia Radostin Simitev, Friedrich Busse University of Bayreuth, Germany Cellular Dynamo in a Rotating Spherical Shell Alexander Getling Lomonosov Moscow State University Moscow, Russia Radostin Simitev, Friedrich Busse University of Bayreuth, Germany

2. The problem of solar dynamo: interplay between global and local magnetic fields needs to be included Mean-field electrodynamics → no local fields considered no local fields considered Possible alternative → “deterministic” dynamo with well-defined “deterministic” dynamo with well-defined structural elements in the flow and structural elements in the flow and magnetic field magnetic field

3. Kinematic model of cellular dynamo (cell = toroidal eddy): A.V. Getling and B.A. Tverskoy, Geomagn. Aeron. 11, 211, 389 (1971)

4. Convective mechanism of magnetic-field amplification and structuring

5. This study is based on numerical simulations of cellular magnetoconvection in a rotating spherical shell

6. The problem Spherical fluid shell Spherical fluid shell Stress-free, electrically insulating boundaries with perfect heat conductivity Stress-free, electrically insulating boundaries with perfect heat conductivity Uniformly distributed internal heat sources Uniformly distributed internal heat sources Boussinesq approximation Boussinesq approximation A small quadratic term is present in the temperature dependence of density A small quadratic term is present in the temperature dependence of density

7. The geometry of the problem

8. Static temperature profile

9. Physical parameters of the problem

10. The case discussed here Geometrical parameter: η = 0.6 Physical parameters: R i = 3000, R e = − 6000, τ = 10, P = 1, P m =30 Computational parameter: m = 5

11. Static profiles of temperature and its gradient

12. Pseudospectral code employed: F.H. Busse, E. Grote, and A. Tilgner, Stud. Geophys. Geod. 42, 211 (1998)

13. Radial velocity at r = r i + 0.5 d t = 98.73

14. Azimuthal velocity and meridional streamlines t = 98.73

15. Radial magnetic field at r = r o + 0.7 d t = 98.73t = 101.73

16. Radial magnetic field at r = r o

17. Azimuthal magnetic field and meridional field lines t = 95.73t = 101.73

18. Variations in poloidal components H 1 0 and H 2 0 at r = 0.5

19. Variations in full magnetic energy

20. Variations in dipolar-field energy axisymm. pol. axisymm. tor. asymm. pol. asymm. tor.

21. Thank you for your attention