Deep magnetic field stretching in numerical dynamos

Progress in Earth and Planetary Science

Table 2 Global statistics at mid-depth: dynamo models time average and standard deviation values

Model	Ad_r/Ad_h	St_r/St_h	St_h/Ad_h	St/Ad	\(\mathcal {P}/\mathcal {T}\)	\(\\|u_{r}\\|/\\|\vec {u}_{h}\\|\)
1	0.63±0.05	1.33±0.22	0.44±0.05	0.78±0.16	0.37±0.04	0.69±0.06
2	0.60±0.10	1.26±0.20	0.41±0.07	0.66±0.10	0.38±0.04	0.71±0.04
3	0.63±0.08	1.29±0.18	0.38±0.06	0.65±0.12	0.43±0.03	0.76±0.10
4	0.50±0.07	1.76±0.22	0.43±0.08	0.90±0.12	0.32±0.04	0.60±0.06
5	0.52±0.07	1.45±0.17	0.48±0.07	0.85±0.09	0.38±0.03	0.65±0.06
6	0.64±0.07	1.25±0.15	0.50±0.05	0.81±0.10	0.42±0.05	0.75±0.05
7	0.57±0.08	1.27±0.11	0.64±0.11	1.00±0.14	0.38±0.03	0.71±0.06
8	0.59±0.05	1.29±0.13	0.56±0.04	0.88±0.13	0.42±0.05	0.74±0.07
9	0.65±0.04	1.14±0.07	0.52±0.05	0.75±0.06	0.44±0.04	0.79±0.05

St_r, St_h, and St are the radial, tangential, and total stretching rms, respectively; Ad_r, Ad_h, and Ad are the radial, tangential, and total advection rms, respectively; \(\mathcal {P}/\mathcal {T}\) is the poloidal/toroidal flow rms ratio, and \(\|u_{r}\|/\|\vec {u}_{h}\|\) is the radial/tangential flow rms ratio