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 |