Gravitational dynamos and the low-frequency geomagnetic secular variation

Olson. 10.1073/pnas.0709081104

Supporting Information

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SI Figure 8
SI Figure 9
SI Figure 10
SI Figure 11
SI Table 1
SI Movie 1
SI Movie 2
SI Figure 12
SI Figure 13




SI Figure 8

Fig. 8. Power spectra of the nonreversing gravitational dynamo shown in Fig. 3. Frequency axes are dipole decay frequency units. (Upper Left) rms internal magnetic field intensity. (Upper Right) rms dipole field intensity on the core-mantle boundary. (Lower Left) rms dynamo velocity in magnetic Reynolds number units. (Lower Right) rms axial dipole field intensity on the core-mantle boundary. Dashed vertical lines denote velocity corner frequency; solid lines indicate various power law slopes





SI Figure 9

Fig. 9. Dipole field power spectra from four additional gravitational dynamos, chosen to illustrate various parameter dependence, including lower magnetic Prandtl number, lower Ekman number, and higher Rayleigh number. Frequency axes are scaled by the dipole decay frequency. Dashed vertical lines denote velocity corner frequency for each case; solid lines indicate various power law slopes for reference. Note that the spectra have similar shape when scaled in terms of magnetic dipole decay time units, despite the large differences in Rayleigh, Ekman, and magnetic Prandtl numbers. Each spectrum is flat at very low frequency, has a best fitting slope of n = -2 or -7/3, and all show evidence of corners or knees which are prominent in their respective velocity spectra and correspond approximately to the free decay time of the main toroidal field in these models. Above the corner frequency, the spectral slopes are all large, in the range of n = -4. In addition, the longest-run case shows particularly good evidence of spectral flattening at low frequencies.





SI Figure 10

Fig. 10. High-pass-filtered segment of the time series of the reversing gravitational dynamo shown in Fig. 2. Shown from top to bottom are rms dipole strength (unfiltered); rms velocity (filtered); rms dipole strength (filtered); comparison of filtered dipole (broken)and filtered velocity (solid) during a polarity excursion.





SI Figure 11

Fig. 11. Dipole field versus local Rossby number for the gravitational dynamos. Time average values are denoted by circles, standard deviations are indicated by error bars. Closed and open circles denote reversing and nonreversing dynamos, respectively.





SI Figure 12

Fig. 12. Time variation of the geomagnetic dipole moment since 2 Ma determined from relative magnetic intensity of deep sea sediments [from Valet et al. (1)]. Normal and reverse magnetic polarity chrons and excursions are indicated by dark and light shading, respectively. Dashed line indicates present-day dipole moment.

1. Valet J-P, Meynadier L, Guyodo Y (2005) Nature 435:802-805.





SI Figure 13

Fig. 13. Geomagnetic dipole moment power spectral estimates compared with reversing gravitational dynamo dipole moment power spectrum. The curve labeled CJ 05 is the Constable and Johnson (1) composite geomagnetic power spectrum; the curve labeled VMG 05 is the paleomagnetic spectrum according to Valet et al. (2) from Fig. 12. The dynamo model spectrum amplitude (gray) is scaled to match the observed geomagnetic variance and its frequency is scaled assuming fd = 50/Myr, marked by vertical line.

1. Constable C, Johnson C (2005) Phys Earth Planet Interiors 153:61-73.

2. Valet J-P, Meynadier L, Guyodo Y (2005) Nature 435:802-805.





SI Movie 1

Movie 1. Animation of a magnetic polarity reversal from the gravitational dynamo shown in Figs. 2, 4, and 6. Shown is the radial magnetic field on the core-mantle boundary over one dipole decay time. The red cross marks the geomagnetic dipole axis.





SI Movie 2

Movie 2. Animation of a magnetic polarity reversal from the gravitational dynamo shown in Figs. 2, 4, and 6. Shown are the light element concentration, axial vorticity, and axial field in the equatorial plane over one dipole decay time.

This Article

  1. Published online before print November 29, 2007, doi: 10.1073/pnas.0709081104 PNAS December 18, 2007 vol. 104 no. 51 20159-20166
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