Box Model:Core Evolution

~ 700 Myr

T(r,t)C(r,t)rICB(t)

3D Model:Numerical Dynamo

~ 5 Myr intervals

T(x,t)C(x,t)B(x,t)

ThermodynamicParameters

CMB Heat Flow Q(t)T(r,0), C(r,0), rICB(0)

Transport ParametersCMB Heat Flux Heterogeneity q(x)

W(t)

GPTSReversals

Geodynamo Evolution Flow Chart

Dynamo Equations

(Boussinesq approximation w/ thermo-chemical convection)

Navier-Stokes:

Induction:

Continuity: Transport:

Co-density (temperature + light elements):

Self-sustaining dynamo: finite magnetic energy w/o external sources

Dynamo Parameters ----- Inputs -------

Earth’s Core Dynamo Models(Numerical, Laboratory)

E (Ekman #) rotational constraint

10-9 (turbulent)10-13 (laminar)

10-3 - 10-7

> 10-5

Ra (Rayleigh #) convective forcing

1020 - 1030 104 - 1010

mechanical forcing

Pr (Prandtl #) viscous/ thermal diffusion

0.1 - 1 ~ 1~ 0.1

Pm (magnetic Prandtl #) viscous/magnetic diffusion

----- Outputs ------------

10-5 - 10-6 0.1 - 20~ 10-5

Rm (magnetic Reynolds #) fluid velocity

300 - 1000 40(critical) - 1000< 100

(Elsasser #) magnetic energy density

0.1 - 1 0.1 - 10.1 - 1

Rol (local Rossby #)

turbulence

~0.1 0.01 - 0.1 1 - 100

Numerical Dynamo Resolution vs. Simulation Time

* Magnetic free decay time, NOT astronomical time!

*

Realism

Efficiency