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Geodynamo Benchmarks
Historical Benchmark Cases
There are two cases defined in the benchmark study published in the 2001 paper by Christensen et al. Case 0 is a benchmark of rotating non-magnetic convection. Case 1 is a dynamo with an insulating inner core co-rotating with the outer boundary. The regions outside the fluid shell are electrical insulators and the magnetic field on the boundaries matches with appropriate potential fields in the exterior that imply no external sources of the field.
In both cases the Ekman number is [;E = 10^{-3};] and the Prandtl number is [;Pr = 1;]. The Rayleigh number is set to [;Ra = 100000;]. Note that the definition of the Rayleigh number differs from the one in the published cases by a factor of Ekman number [;E;], i.e., [;Ra=\frac{Ra}{E};]. The magnetic Prandtl number is zero in the non-magnetic convection case 0, and is [;Pm = 5;] in case 1. The spherical harmonic expansion is truncated at degree [;lmax=32;] and a four-fold symmetry is assumed in the longitudinal direction (the file param.f should be linked to param32s4.f when you compile MAG). The input parameter files are par.bench0 for case 0, and par.bench1 for case 1; both files reside in the ~/src directory.
The output files of the benchmark cases are stored in the directory ~/bench-data/data_bench0 and ~/bench-data/data_bench1 respectively. In the following table we see the solutions from MAG agree with the benchmark suggested value with a small margin of difference. In both case 0 and case 1, the values listed were obtained with low resolution and a relatively short run of MAG.
| Case 0 Suggested value | Mag Case 0 | Case 1 Suggested Value | Mag Case 1 | |
| [;E_{kin};] | 58.348 ± 0.050 | 58.35 | 30.733 ± 0.020 | 30.72 |
| [;E_{mag};] | 626.41 ± 0.40 | 627.15 | ||
| [;T;] | 0.42812 ± 0.00012 | 0.37338 ± 0.00040 | ||
| [;\mu_{\phi};] | -10.1571 ± 0.0020 | -10.80 | -7.6250 ± 0.0060 | -7.84 |
| [;B_{\theta};] | -4.9289 ± 0.0060 | |||
| [;\omega;] | 0.1824 ± 0.0050 | -3.1017 ± 0.0040 |
Reversal Dynamo Case
In this benchmark, we produce a magnetic field reversal using MAG. The input parameter in the source directory for this case is ~/src/par.Rev. There is no longitudinal symmetry in this case, so when you compile MAG, use param32s1.f linking to param.f. The Ekman number is [;E=0.02;], the Prandtl number is [;Pr=1;] and the magnetic Prandtl number is [;Pm=10;]. The Rayleigh number is [;Ra=12000;].
Results and Discussions
This case was run on 32-bit and 64-bit Intel processors. Figure F1 shows a plot of mean velocity Vrms, mean magnetic field Brms, the axial dipole and the dipole tilt on the outer boundary. It indicated a magnetic field reversal between times 25 and 30. Figure F2 shows a longer run of MAG, where we see the magnetic field reversed again. At this time, the magnetic field had weakened substantially. In Figure P1 and Figure P2, the top is the pole plot before the second field reversal and the bottom is the pole plot after the second field reversal.
Figure F1: Field Plot for Reversal Dynamo Case
Figure F2: Field Plot for Reversal Dynamo Case (longer run)
Figure P1: Magnetic field pole plot, at the beginning of the second field reversal.
Figure P2: Magnetic field pole plot, at the end of the second field reversal.
