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Table 6 Variables used in this paper

From: Magnetic field stretching at the top of the shell of numerical dynamos

Symbol Meaning
\(\vec {u}\) Velocity
\(\vec {B}\) Magnetic field
t Time
P Pressure
T Temperature (or co-density)
\(\epsilon \) Heat (or buoyancy) source or sink
Ra Rayleigh number
E Ekman number
Pr Prandtl number
Pm Magnetic Prandtl number
Rm Magnetic Reynolds number
Rm a Effective advective magnetic Reynolds number
Rm s Effective stretching magnetic Reynolds number
Rm e Effective magnetic Reynolds number
α Thermal expansivity
g o Gravitational acceleration on the outer boundary at radius r o
q o Mean heat flux across the outer boundary
D Shell thickness
k Thermal conductivity
κ Thermal diffusivity
ν Kinematic viscosity
Ω Rotation rate
λ Magnetic diffusivity
U Typical velocity scale
L Typical length scale
\(\hat{z}\) Unit vector in the direction of the rotation axis
r Radial coordinate
\(\hat{r}\) Unit vector in the radial direction
\(\vec {r}\) Position vector
r o Earth’s core radius
r e Radial level at which the simulations were analyzed
\(\bar{\delta \tau }\) Average time difference between snapshots in units of magnetic advection time
B r Radial component of the magnetic field on the CMB
\(\vec {u}_{h}\) 2D velocity vector tangent to the CMB spherical surface
St/Ad Ratio of stretching RMS to advection RMS
\({\mathcal {P}}/{\mathcal {T}}\) Ratio of poloidal flow RMS to toroidal flow RMS
δ h Tangential divergence
ω r Radial vorticity
H u Helical flow correlation
\(\delta _h^-\) Downwelling process (δ h < 0)
\(\delta _h^+\) Upwelling process (δ h > 0)
ξ a Normalized integrated advective
ξ s Normalized integrated stretching
ξ e Normalized integrated magnetic field intensification by stretching
γ Angle between the vectors \(\vec {u}_h\) and \(\nabla _h B_r\)
cos γ Field–flow alignment factor
ξ Rm Advection/stretching interference factor
f Statistical quantity
C, a, b, c Generic power law fitting coefficients
σ r Relative misfit of the power law
f dyn Statistical quantity in dynamo models
n Number of dynamo models analyzed
\({\mathcal {T}}_1\) Large-scale degree-1 toroidal synthetic flow
\({\mathcal {P}}_1\) Large-scale degree-1 poloidal synthetic flow