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Table 7 Parameter dependence: power law fits and relative misfit σ r

From: Deep magnetic field stretching in numerical dynamos

Quantity Type Mid-shell σ r δ σ r Outer boundary
Ad r /Ad h Global \(0.738 \cdot (E^{2} \cdot Ra)^{\frac {1}{8}}\) 0.029 0.004
  HN \(0.580 \cdot (E^{2} \cdot Ra)^{-\frac {1}{11}}\) 0.042 0.000
St r /St h Global \(2.081 \cdot (E^{3} \cdot Ra^{2} \cdot Pm)^{-\frac {1}{12}}\) 0.054 0.007
  HN \(2.982 \cdot (E \cdot Ra^{2} \cdot Pm)^{-\frac {1}{28}}\) 0.080 0.000
St h /Ad h Global \(0.628 \cdot Pm^{-\frac {1}{4}}\) 0.071 0.004 \(2.996 \cdot (E \cdot Ra \cdot Pm^{3})^{-\frac {1}{6}}\)
  HN \(0.765 \cdot (E^{6} \cdot Ra^{3} \cdot Pm^{5})^{-\frac {1}{11}}\) 0.140 0.005 \(10.489 \cdot (E \cdot Ra \cdot Pm^{2})^{-\frac {1}{3}}\)
St/Ad Global \(1.666 \cdot (E^{4} \cdot Ra^{3} \cdot Pm^{6})^{-\frac {1}{24}}\) 0.036 0.004 \(2.996 \cdot (E \cdot Ra \cdot Pm^{3})^{-\frac {1}{6}}\)
  HN \(0.425 \cdot (E^{9} \cdot Ra^{4} \cdot Pm^{3})^{-\frac {1}{13}}\) 0.184 0.016 \(10.489 \cdot (E \cdot Ra \cdot Pm^{2})^{-\frac {1}{3}}\)
\(\mathcal {P}/\mathcal {T}\) Global \(0.302 \cdot (E^{3} \cdot Ra^{2})^{\frac {1}{16}}\) 0.035 0.002 \(0.319 \cdot Pm^{\frac {1}{6}}\)
  HN \(0.105 \cdot (E^{-1} \cdot Pm)^{\frac {1}{8}}\) 0.089 0.002 \(0.261 \cdot Pm^{\frac {1}{6}}\)
\(\|u_{r}\|/\|\vec {u}_{h}\|\) Global \(0.556 \cdot (E^{3} \cdot Ra^{2})^{\frac {1}{16}}\) 0.025 0.005
  HN \(0.117 \cdot (Ra^{3} \cdot Pm^{5})^{\frac {1}{20}}\) 0.078 0.003
  1. The fit deterioration is defined by δσ r =σ r σ ro where σ ro is the initial best fit relative misfit. Quantities are the same as in Table 2. Also given are the power laws for the outer boundary (Peña et al. 2016)