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 |