1. Geodynamics VI Core Dynamics and the Magnetic Field Bruce Buffett, UC Berkeley

2. er General Objectives How do fluid motions in liquid core generate a magnetic field?

3. Planetary Perspective planetary dynamos are sensitive to the internal state

4. Did the Early Earth have a Magnetic Field ?

5. Observations NASA 1. Paleomagnetic evidence of a magnetic field at 3.45 Ga (Tarduno et al. 2009) 2. Measurement of 15 N/ 14 N ratio in lunar soil (Ozima et al. 2005) - no field before 3.9 Ga ? Implications for the early Earth? (probably tells us about tectonics)

6. Outline 2. Thermal evolution and dynamo power 3. Convection in core 4. Generation of magnetic field numerical models 1. Physical setting and processes

7. Physical Processes Cooling of the core is controlled by mantle convection contraction Present day

8. Present-Day Temperature temperature drop across D”:  T = 900 - 1900 K D”D”

9. Core Heat Flow ~ 5 to 10 TW thermal boundary layer on the core side? 900 – 1900 K adiabat

10. Core Heat Flow ~ 5 to 10 TW ~ 3 to 5 TW conduction along adiabat is comparable to mantle heat flow

11. Core Heat Flow ~ 5 to 10 TW ~ 3 to 5 TW conduction along adiabat is comparable to total heat flow 10 to 15 TW

12. Convection in the Core Fe alloy Q > Q a cold thermal boundary layer

13. Convection in the Core Q < Q a i) compositional buoyancy mixes warm fluid ii) thermally stratified layer develops Options

14. Early Earth i) Q < Q a - geodynamo fails * - convection ceases - a geodynamo is possible ii) Q > Q a * core-mantle (chemical) interactions might help

15. Chemical Interactions Early Earth Cooling reduces solubility of mantle components Energy Supply depends on - abundance of element - T-dependence of solubility O and/or Si appear to be under saturated at present

16. Growth of Inner Core Based on energy conservation t Often assumes that the core evolves through a series of states that are hydrostatic, well-mixed and adiabatic

17. Growth of Inner Core Based on energy conservation Heat budget includes - secular cooling - radioactive heat sources - latent heat - gravitational energy* t *due to chemical rearrangement *

18. Example Inner-core RadiusCMB Temperature based on Buffett (2002)

19. Power Available for Geodynamo dissipation Entropy Balance Carnot efficiency convection

20. Carnot Efficiencies Dynamo Power  thermallatent heatcomposition

21. Carnot Efficiencies Dynamo Power  thermallatent heatcomposition Example using Q cmb = 6 TW i)Present day  = 1.3 TW ii)Early Earth  = 0.1 TW

22. Carnot Efficiencies Dynamo Power  thermallatent heatcomposition Example using Q cmb = 6 TW i)Present day  = 0.8 TW ii)Early Earth  = 0.1 TW

23. Average Digression on Thermal History Convective Heat Flux where This means that q conv is independent of L

24. A thermal dynamo on early Earth? (a) Two regimes for i) Pre-Plate tectonics (T m > 1500 o C) ii) Plate tectonics (T m < 1500 o C) (b) CMB Heat Flux evidence of a field by 3.45 Ga (Sleep, 2007) (a) (b) TmTm TcTc

25. A Thermal History Mantle TemperatureCMB Heat Flux (i) (ii) Q = 76 TW evidence of field decreasing radiogenic heat Implications: a) vigorous dynamo during first (few) 100 Ma (dipolar?) b) narrow range of parameters allow the dynamo to turn off

26. Numerical Models Glatzmaier & Roberts (1996) magnetic fieldvertical vorticity Numerical Models

27. Description of Problem 1. Conservation of momentum (1687) 2. Magnetic Induction (1864) 3. Conservation of Energy (1850) Newton Maxwell Fourier

28. Convection in Rotating Fluid 1. Momentum equation (ma = f) Coriolisbuoyancyviscous Character of Flow

29. Taylor-Proudman Constraint 1. Momentum equation (ma = f) Introduce vorticity V Radial component requiresa buoyant parcel will not rise

30. Taylor-Proudman Constraint 1. Momentum equation (ma = f) Introduce vorticity V Radial component requires

31. Taylor-Proudman Constraint 1. Momentum equation (ma = f) Introduce vorticity V Radial component requires

32. Planetary Dynamo Vertical Vorticity E = 5 x 10 -5

33. Are dynamo models realistic(1) ? A popular scaling is based on the assumption that viscosity is unimportant dynamo simulations appear to be controlled by viscosity (King, in prep)

34. Are dynamo models realistic(2)? Da Vinci, 1509 “Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity” Richardson, 1922 Viscosity  (i.e. momentum diffusion) limits the length scale of flow Magnetic diffusion (  ) limits the length scale of field

35. Properties of the Liquid Metal Viscosity  ~ 10 -6 m 2 /s Thermal Diffusivity  ~ 10 -5 m 2 /s Magnetic Diffusivity  ~ 1 m 2 /s Prandtl Numbers

36. Characteristic Scales (Sakuraba and Roberts, 2009) Velocity (radial) Magnetic Field (radial) E = 3x10 -6 P m = 0.1

37. Exploit Scale Separation? use realistic properties in a small (10 km) 3 volume

38. Model Geometrytemperature 256x128x64 Small-Scale Convection Use structure of small-scale flow to construct “turbulent” dynamo model ?

39. Summary The existence or absence of a field tells us about the dynamics of the mantle, the style of tectonics and the vigor of geological activity. All viable thermal history models need to satisfied the observed constraint Earth had a field by 3.45 Ga We have seen remarkable progress in dynamo models in the last decade. We probably have a long way to go, although that view is not accepted by everyone in the geodynamo community.