Geomagnetism a dynamo at the centre of the earth l.jpg
This presentation is the property of its rightful owner.
Sponsored Links
1 / 35

GEOMAGNETISM: a dynamo at the centre of the Earth PowerPoint PPT Presentation


  • 198 Views
  • Uploaded on
  • Presentation posted in: General

GEOMAGNETISM: a dynamo at the centre of the Earth. Lecture 1 How the dynamo is powered Lecture 2 How the dynamo works Lecture 3 Interpreting the observations Lecture 4 Thermal core-mantle interactions. Lecture 1 How the dynamo is powered.

Download Presentation

GEOMAGNETISM: a dynamo at the centre of the Earth

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Geomagnetism a dynamo at the centre of the earth l.jpg

GEOMAGNETISM: a dynamo at the centre of the Earth

  • Lecture 1 How the dynamo is powered

  • Lecture 2 How the dynamo works

  • Lecture 3 Interpreting the observations

  • Lecture 4 Thermal core-mantle interactions


Lecture 1 how the dynamo is powered l.jpg

Lecture 1How the dynamo is powered

  • Gubbins, D., D. Alfe, G. Masters, D Price & M.J. Gillan “Can the Earth’s dynamo run on heat alone?”

  • “Gross thermodynamics of 2-component core convection”

  • - both under review for Geophysical Journal International


Energy lost through electrical resistance l.jpg

ENERGY LOST THROUGH ELECTRICAL RESISTANCE

  • Magnetic field decays in 15,000 years

  • Energy loss is 1011 - 1012 W


The model l.jpg

THE MODEL

  • Core cooling drives convection

  • Perhaps some radioactive heating

  • Inner core freezes -> more latent heat…

  • …and releases light material that drives convection through…

  • Release of gravitational energy


Slide5 l.jpg

Mantle

K40

O

H

inner core

latent heat

Fe

S

Si


The basic state l.jpg

THE BASIC STATE

  • Pressure is nearly hydrostatic:

  • Convective velocity >> diffusion…

  • …means core is well mixed

  • …including entropy

  • Temperature is adiabatic


Gruneissen s parameter l.jpg

GRUNEISSEN’S PARAMETER

Thermodynamic definition:

Hydrostatic pressure:

Seismic parameter:


Slide8 l.jpg

Temperature in the core is found by integrating up from

the inner core boundary, where T is the known melting temperature

Time evolution of the (logarithm) of temperature is then

the same everywhere:


Inner core freezing l.jpg

INNER CORE FREEZING


The first twist l.jpg

THE FIRST TWIST...

Conservation of energy does not equate the energy required with the heat lost by the magnetic field, in fact it does not involve the magnetic field at all!


Energy flow chart l.jpg

ENERGY FLOW CHART

dynamo

conduction +

convection

electricalheating

buoyancy

expansion


Entropy balance l.jpg

ENTROPY BALANCE

Dissipation gives entropy gains:

  • thermal conduction

  • electrical conduction

    Offset by entropy losses if Tin>Tout


Backus ideal dynamo l.jpg

BACKUS’ IDEAL DYNAMO

“Efficiency” :

  • Can be greater than unity.

  • This is because the output of the heat engine, the electrical heating, is used again in powering the convection.

  • A Carnot engine driving a disk dynamo achieves the ideal bound


The second twist l.jpg

THE SECOND TWIST...

  • Cooling and contraction releases a significant amount of Earth’s gravitational energy

  • Freezing also releases gravitational energy

  • Is this available to the dynamo? Some think so

  • But only about 5% is available


Gravitational energy l.jpg

GRAVITATIONAL ENERGY

  • Is calculated from the work done in assembling all the mass from infinity

  • The gravitational force is conservative, so we can do this however we like

  • Assemble the mass of the Earth slowly, maintaining hydrostatic pressure

  • Then all of the gravitational energy goes into compaction, except for….

  • …a small amount caused by pressure heating


Pressure heating l.jpg

PRESSURE HEATING

Drop temperature for change in volume

From the Maxwell relation

Heat released

Divide by specific heat released:


Pressure effect on freezing l.jpg

PRESSURE EFFECT ON FREEZING

The change in volume on freezing also releases gravitational energy

The change in volume on freezing is related to the latent heat (L) through the Clausius-Clapeyron equation

Again the only part of this gravitational energy that is available

to drive convection is a small amount of pressure heating


Slide18 l.jpg

The increase in melting temperature caused by the higher causes the inner core to grow a little more

The latent heat released is identically equal to the gravitational energy change, because of the Clausius-Clapeyron equation


Summary heat only l.jpg

SUMMARY - HEAT ONLY

Entropy balance: choose LHS and find cooling rate and radioactive heating h

Energy balance: find heat flux from cooling rate and radioactive heating h


Adiabatic gradients l.jpg

ADIABATIC GRADIENTS


Heat budget l.jpg

HEAT BUDGET

Earth’s heat budget:

Crustal radioactivity9 TW mostly lower crust

mantle radioactivity 25 TWchondritic composition

core radioactivity0 TWiron meteorites, chemistry

cooling 10 TW includes core, mantle

TOTAL 44 TW Surface heat flux

Cooling rate: 36 K/GyrFrom core 3 TW


Results for thermal convection l.jpg

RESULTS FOR THERMAL CONVECTION

MODELdTc/dt dri/dtICage QLQSQ

K/Gyr km/GyrMaTWTWTW

GAMP02214 141428810.210.921.6

LPL97234 15502638.414.223.0

NOIC565 0.028.828.8

Comparison between 3 models of Gubbins et al 2002;

LaBrosse et al 1997 (modified); and a model with no inner core (L=0)


Compositional convection l.jpg

COMPOSITIONAL CONVECTION

  • Light material released at the inner core boundary on freezing rises to stir the core

  • Energy source is Earth’s gravitational energy

  • This changes as light material rises, heavy iron sinks

  • Compositional convection stirs the core directly, there is no thermal efficiency factor


Slide25 l.jpg

Mantle

K40

O

H

inner core

latent heat

Fe

S

Si


The story so far l.jpg

THE STORY SO FAR...

  • Thermal convection cannot drive the dynamo because too much heat is needed

  • This means we have no means of generating a magnetic field before the inner core formed, the inner core must be as old as the magnetic field

  • Compositional convection can help drive the dynamo

  • The solid inner core can include 8% S or Si to explain the density. When this mixture freezes, it all freezes.

  • A liquid Fe+8%S+8% O can explain the density of the liquid outer core

  • When Fe+8%O mixture freezes, the O is left in the liquid

  • This provides the source of buoyancy for compositional convection


Slide28 l.jpg

NEXT...

  • We see if compositional plus thermal convection can drive the dynamo

  • We estimate the cooling rates and radioactive heating needed by balancing the entropy

  • Then we use the cooling rate and radioactive heating to calculate the heat flux across the core-mantle boundary and the inner core age.


Core composition of price alfe gillan 2001 l.jpg

CORE COMPOSITION OF PRICE, ALFE & GILLAN (2001)


Density reductions from pure iron at icb pressure and temperature l.jpg

DENSITY REDUCTIONS FROM PURE IRON AT ICB PRESSURE AND TEMPERATURE

r%Dr

Solid iron13.16

8% S/Si12.763.0%0.40

Melting12.521.8%0.24

8%O12.172.8%0.37

Ideal solutions theory predicts densities well, but not diffusion

constants or free energies


Dissipation entropy l.jpg

DISSIPATION ENTROPY

  • Thermal conduction 200-500 MW/K

  • Ohmic heating 50-500 MW/K

  • Molecular diffusion 1 MW/K

  • Round up 1000 MW/K


Final equations l.jpg

FINAL EQUATIONS

Find the cooling rate and radioactive heating from the entropy balance

And find the heat flux from cooling rate and radioactive heating


The models l.jpg

THE MODELS

  • E = 1000 MW/K “rounding up”

  • E= 546 MW/K, heat conducted down by compositional convection

  • E = 262 MW/KDynamo fails

  • Repeat with enough radioactive heating to make the inner core last 3.5 Gyr


Results for compositional convection l.jpg

RESULTS FOR COMPOSITIONAL CONVECTION


Conclusions l.jpg

CONCLUSIONS

  • Compositional convection only doubles the efficiency of the dynamo

  • With present estimates and no radioactivity in the core, the age of the inner core is less than 1Ga

  • The simplest way to alter this result is to increase the seismological estimate of the density jump at the inner core boundary

  • At present it seems impossible to drive the dynamo without an inner core


  • Login