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Geodynamics VI Core Dynamics and the Magnetic Field. Bruce Buffett, UC Berkeley. er. General Objectives. How do fluid motions in liquid core generate a magnetic field?. Planetary Perspective. planetary dynamos are sensitive to the internal state. Did the Early Earth have a Magnetic Field ?. - PowerPoint PPT Presentation
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Geodynamics VI
Core Dynamics and the Magnetic Field
Bruce Buffett, UC Berkeley
er
General Objectives
How do fluid motions in liquid core generate a magnetic field?
Planetary Perspective
planetary dynamos are sensitive to the internal state
Did the Early Earth have a Magnetic Field ?
Observations
NASA
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)
Outline
2. Thermal evolution and dynamo power
3. Convection in core
4. Generation of magnetic field
numericalmodels
1. Physical setting and processes
Physical Processes
Cooling of the core is controlled by mantle convection
contraction
Present day
Present-Day Temperature
temperature drop across D”: T = 900 - 1900 K
D”
Core Heat Flow
~ 5 to 10 TW
thermal boundary layer on the core side?
900 – 1900 K adiabat
Core Heat Flow
~ 5 to 10 TW
~ 3 to 5 TW
conduction along adiabat is comparable to mantle heat flow
Core Heat Flow
~ 5 to 10 TW
~ 3 to 5 TW
conduction along adiabat is comparable to total heat flow
10 to 15 TW
Convection in the Core
Fe alloy
Q > Qa
cold thermal boundary layer
Convection in the Core
Q < Qa
i) compositional buoyancy mixes warm fluid
ii) thermally stratified layer develops
Options
Early Earth
i) Q < Qa
- geodynamo fails *
- convection ceases
- a geodynamo is possible
ii) Q > Qa
* core-mantle (chemical) interactions might help
Chemical Interactions
Early Earth
Cooling reduces solubility ofmantle components
Energy Supply depends on
- abundance of element
- T-dependence of solubility
O and/or Si appear to be under saturated at present
Growth of Inner Core
Based on energy conservation
t
Often assumes that the coreevolves through a series of statesthat are hydrostatic, well-mixed and adiabatic
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
*
Example
Inner-core Radius CMB Temperature
based on Buffett (2002)
Power Available for Geodynamo
dissipation
Entropy Balance
Carnot efficiency
convection
Carnot Efficiencies
Dynamo Power
thermal latent heat composition
Carnot Efficiencies
Dynamo Power
thermal latent heat composition
Example using Qcmb = 6 TW
i) Present day = 1.3 TW
ii) Early Earth = 0.1 TW
Carnot Efficiencies
Dynamo Power
thermal latent heat composition
Example using Qcmb = 6 TW
i) Present day = 0.8 TW
ii) Early Earth = 0.1 TW
AverageDigression on Thermal History
Convective Heat Flux
where
This means that qconv is independent of L
A thermal dynamo on early Earth?
(a) Two regimes for
i) Pre-Plate tectonics (Tm > 1500o C)
ii) Plate tectonics (Tm < 1500o C)(b) CMB Heat Flux
evidence of a field by 3.45 Ga(Sleep, 2007)
(a)
(b)
Tm
Tc
A Thermal History
Mantle Temperature CMB 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
Numerical Models
Glatzmaier & Roberts (1996)
magnetic fieldvertical vorticity
Numerical Models
Description of Problem
1. Conservation of momentum (1687)
2. Magnetic Induction (1864)
3. Conservation of Energy (1850)
Newton
Maxwell
Fourier
Convection in Rotating Fluid
1. Momentum equation (ma = f)
Coriolis buoyancy viscous
Character of Flow
Taylor-Proudman Constraint
1. Momentum equation (ma = f)
Introduce vorticity
V
Radial component requires a buoyant parcelwill not rise
Taylor-Proudman Constraint
1. Momentum equation (ma = f)
Introduce vorticity
V
Radial component requires
Taylor-Proudman Constraint
1. Momentum equation (ma = f)
Introduce vorticity
V
Radial component requires
Planetary DynamoVertical Vorticity
E = 5 x 10-5
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)
Are dynamo models realistic(2)?
Da Vinci, 1509
“Big whirls have little whirlsthat feed on their velocity,and little whirls have lesser whirlsand 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
Properties of the Liquid Metal
Viscosity ~ 10-6 m2/s
Thermal Diffusivity ~ 10-5 m2/s
Magnetic Diffusivity ~ 1 m2/s
Prandtl Numbers
Characteristic Scales
(Sakuraba and Roberts, 2009)
Velocity (radial) Magnetic Field (radial)
E = 3x10-6 Pm = 0.1
Exploit Scale Separation?
use realistic properties in a small (10 km)3 volume
Model Geometry temperature
256x128x64
Small-Scale Convection
Use structure of small-scale flow to construct “turbulent” dynamo model ?
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 constraintEarth 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 byeveryone in the geodynamo community.