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.