Geodynamics VI Core Dynamics and the Magnetic Field

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

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

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

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

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

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 10 to 15 TW conduction along adiabat is comparable to total heat flow

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

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

14. Early Earth i) Q < Qa - convection ceases - geodynamo fails * ii) Q > Qa - a geodynamo is possible * 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 Often assumes that the core evolves through a series of states that are hydrostatic, well-mixed and adiabatic t

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

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

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

20. Carnot Efficiencies Dynamo Power F thermal latent heat composition

21. Carnot Efficiencies Dynamo Power F thermal latent heat composition Example using Qcmb = 6 TW • Present day F = 1.3 TW • Early Earth F = 0.1 TW

22. Carnot Efficiencies Dynamo Power F thermal latent heat composition Example using Qcmb = 6 TW • Present day F = 0.8 TW • Early Earth F = 0.1 TW

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

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

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

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

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

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

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

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

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

32. Vertical Vorticity Planetary Dynamo 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)? “Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity” Richardson, 1922 Da Vinci, 1509 Viscosity n (i.e. momentum diffusion) limits the length scale of flow Magnetic diffusion (h = 1/ms) limits the length scale of field

35. Properties of the Liquid Metal Viscosity n ~ 10-6 m2/s Thermal Diffusivity k ~ 10-5 m2/s Magnetic Diffusivity h ~ 1m2/s Prandtl Numbers

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

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

38. Small-Scale Convection Model Geometry temperature 256x128x64 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.