Simulations of the geodynamo (Graeme)

Link to talk (pdf)

Thermal convection in a rotating spherical shell of weakly compressible fluid (motivated by geodynamo)

Cartesian domain (equivalent to lsphere_in_a_box)

Damping outside boundaries (for velocity and entropy)

Standard MHD with Laplacian diffusion (what's the Reynolds number?)

Polytropic ideal gas with a background state (density and temperature)

Non-equidistant grid outside the shell (step-linear)

Full sphere and half-sphere runs. Mag field boundaries: Btan=0, d(Bn)/dn=0. (Has to be adapted for spherical coordinates.)

Comparison with Kageyama & Sato, Phys Plasmsas, 1995 (KS95). Early results (McMillan and Sarson, PEPI, 2005) are not correct due to scaling glitch. (cp=1 and R=2/5 were hard-coded in the Pencil Code at that time, before the EquationOfState module was developed.)

Weak dependence of vorticity on the polar direction for non-magnetic convection.

When putting the magnetic field with small magnetic diffusivity (high Rm), dynamo action is obtained. At higher Rm, the simple convection roll pattern is disrupted.

There is a dynamo benchmark in the geodynamo community (Christensen et al., PEPI, 2001), but just for the Boussinesq case . Unfortunately this is not a stable state for a compressible gas.

Qualitatively speaking, the results are similar to another dynamo benchmark.

Future work:

• tidy up and publish (good plan)
• further investigate reversing solutions

• Boussinesq and anelastic fluids
• spherical coordinates
• insulating boundary conditions
• make Coriolis force implicit
  

• Local box simulations of geodynamo