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.

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Presentation transcript:

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

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 (turbulent) (laminar) > Ra (Rayleigh #) convective forcing mechanical forcing Pr (Prandtl #) viscous/ thermal diffusion ~ 1 ~ 0.1 Pm (magnetic Prandtl #) viscous/magnetic diffusion Outputs ~ Rm (magnetic Reynolds #) fluid velocity ( critical ) < 100  (Elsasser #) magnetic energy density Ro l (local Rossby #) turbulence ~

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