1. Box Model: Core Evolution ~ 700 Myr T(r,t) C(r,t) r ICB (t) 3D Model: Numerical Dynamo ~ 5 Myr intervals T(x,t) C(x,t) B(x,t) T(x,t) C(x,t) B(x,t) Thermodynamic Parameters CMB Heat Flow Q(t) T(r,0), C(r,0), r ICB (0) Transport Parameters CMB Heat Flux Heterogeneity q(x)  (t) GPTS Reversals Geodynamo Evolution Flow Chart

2. 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

3. 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 10 20 - 10 30 10 4 - 10 10 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 - 100040( critical ) - 1000 < 100  (Elsasser #) magnetic energy density 0.1 - 1 Ro l (local Rossby #) turbulence ~0.1 0.01 - 0.1 1 - 100

4. Numerical Dynamo Resolution vs. Simulation Time * Magnetic free decay time, NOT astronomical time! * Realism Efficiency