the origin of the earth's magnetic field author: stanislav vrtnik adviser: prof. dr. janez...
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The origin of the Earth's The origin of the Earth's magnetic fieldmagnetic field
Author: Stanislav VrtnikAuthor: Stanislav VrtnikAdviser: prof. dr. Janez DolinšekAdviser: prof. dr. Janez Dolinšek
March 13, 2007March 13, 2007
OutlineOutline
11 IntroductionIntroduction
2 2 Structure of the EarthStructure of the Earth
3 3 The self-excited dynamoThe self-excited dynamo
4 4 An Earth-like numerical dynamo modelsAn Earth-like numerical dynamo models
5 5 The approaching polarity reversalThe approaching polarity reversal
6 6 ConclusionsConclusions
11 IntroductionIntroduction
Geomagnetic field is generated in Earth’s core Temperatures > 3000 K; above Curie point (Tc(Fe) = 1043 K; Tc(Ni) = 627 K )
Magnetic field is generated by electrical current Unsustained electrical current would dissipate within 20.000 years
Paleomagnetic records (ancient field recorded in sediment and lavas ) Earth’s magnetic field exists millions of years Mechanism that regenerates electrical currents (self-excited dynamo) The polarity reversal Earth will lose magnetic shield for high-energy particles
The mantle:The mantle:
2900 km thick
Silicate rocks (with Fe, Mg)
Solid, but ductile can flow on large timescale
Convection of the material moves tectonic plates
Pressure increase with depth and change viscosity
Lower mantle flow less easily
2 Structure of the Earth2 Structure of the Earth
Crust
Not to scale
To scale
Upper mantle
Lower mantle
Liquid outer core
Solid inner core
The Crust:The Crust:
5-70 km tick
< 1% Earth’s volume
100 millions years old
Some grains are 4.4 billion years old
Part of the lithosphere divided on tectonic plates
TheThe outer outer corecore::
2180 km tickLiquid
Fe, Ni, some light elements
TheThe inner inner corecore::
Radius of 1220 kmSolid (Fe, Ni)
3 The self-excited dynamo3 The self-excited dynamo
Self-excited dynamo model was first proposed by Sir Joseph Larmor in 1919
Magnetic instability → (perturbation of the field is exponentially amplified)
Simple experiment with mechanical disk device
2rB
22
rBdxxBU
2r
0
FaradFaradaay disk dynamoy disk dynamo
Magnetic flux through the disk:
Induced voltage:
3 The self-excited dynamo3 The self-excited dynamo
Permanent magnet → replaced with solenoid
Magnetic flux through the disk:
IM
2
IMU
Induced voltage:
Electrical current is given by:
2
IMIR
dt
dIL
R - electrical resistivity of the complete circuit
Self-excited dynamo
3 The self-excited dynamo3 The self-excited dynamo
Electrical current is given by:
2
IMIR
dt
dIL
Solution of the differential equation is:
R
2
ML/t
0eII
System becomes unstable when: M
Rc
2
( < C) the resistivity will damp any initial magnetic perturbation
( < C) the system undergoes a bifurcation →an initial perturbation of the field will be exponentially amplified
A)A)
B)B)
4 4 An Earth-like numerical dynamo modelsAn Earth-like numerical dynamo models
Nonlinear three-dimensional model is needed
Geodynamo operates in ‘strong field’ regime: nonlinear magnetic Lorentz force ≈ Coriolis force → Lorentz force cannot be treated as perturbation → nonlinear numerical computation is required
Cowling’s theorem: self-sustained magnetic field produced by a dynamo cannot be axisymmetric → no 2D solution can be sought → problem has to be investigated directly in 3D
4.1 The m4.1 The magnetohydrodynamics Equationsagnetohydrodynamics Equations
Induction equation:
BBvt
B
2)( B
- magnetic field
v
- velocity
0/1 - the magnetic diffusivity interaction diffusion
0v magnetic field decreases exponentially (Earth = 20.000 years)
magnetic field is "frozen" into the conducting fluid
A)A)
B)B)
4.1 The m4.1 The magnetohydrodynamics Equationsagnetohydrodynamics Equations
Navier-Stokes equation:
- mass density
p - scalar pressure
- viscosity
fv)v(p)vvt
v( 2
31
f
- external forces: Lorentz force
gravity forceCoriolis forcebuoyancy force
To simulate the geodynamo we also need equations for: the gravity potentialthe heat flow
Model for geodynamo can have up to 10 equations
4.2 3D simulation of a geomagnetic field4.2 3D simulation of a geomagnetic field
Glatzmaier-Roberts model:with the dimensions, rotate rate, heat flow and the material properties of the Earth’s core
Time step: 20 days
Simulation now spans more than 300.000 years
The simulation took several thousand CPU hours on the Cray C-90 supercomputer
Yellow - where the fluid flow is the greatest.
The core-mantle boundary - blue the inner core boundary - red G.A. Glatzmaier and P.H. Roberts
4.2 3D simulation of a geomagnetic field4.2 3D simulation of a geomagnetic field
Magnetic field is similar to the Earth's field:
•Intensity of the dipole moment•A dipole dominated structure •Westward drift of the non-dipolar field at the surface (0.2° per year)
G.A. Glatzmaier G.A. Glatzmaier && P.H. Roberts P.H. Roberts
4.2 3D simulation of a geomagnetic field4.2 3D simulation of a geomagnetic field
Middle of reversal
•36.000 years into the simulation magnetic dipole underwent polarity reversal•over a period of a 1000 years. •the magnetic dipole moment decreases down to 10%•recovered immediately after•consistent with the paleomagnetic records
G.A. Glatzmaier & P.H. RobertsG.A. Glatzmaier & P.H. Roberts
500 yr before 500 yr after
a) b) c)
4.2 3D simulation of a geomagnetic field4.2 3D simulation of a geomagnetic field
•The longitudinal average of the 3D magnetic field (out to the surface)
•Left – lines of force of the poloidal part of the field•Right – contours of the toroidal part of the field•Red (blue) contours – eastward (westward) directed toroidal field•Green (yellow) lines – clockwise (anticlockwise) poloidal field
G.A. Glatzmaier G.A. Glatzmaier && P.H. Roberts P.H. Roberts, Nature, 377, 203-209 , Nature, 377, 203-209 (1995) (1995)
5000 yr before Middle of reversal 4000 yr after
4.2 3D simulation of a geomagnetic field4.2 3D simulation of a geomagnetic field
•The radial component of the magnetic field (Hammer projection) •Upper plots (surface); lower plots (core-mantle boundary)•Red (blue) contours represent outward (inward) directed field•Intensity at the surface is multiplied by 10
G.A. Glatzmaier G.A. Glatzmaier && P.H. Roberts P.H. Roberts, Nature, 377, 203-209 (1995), Nature, 377, 203-209 (1995)
4.2 3D simulation of a geomagnetic field4.2 3D simulation of a geomagnetic field
Rotation of the inner core relative to the surface:
•In simulation rotates 2° to 3° per year faster than at the surface•Motivated seismologists to search for evidence (0.3° to 0.5° year faster )•The field couples the inner core to the eastward flowing fluid
•analogous to a synchronous electric motor
G.A. Glatzmaier & P.H. RobertsG.A. Glatzmaier & P.H. Roberts
55 The approaching polarity reversal The approaching polarity reversal
•Study of the geodynamo has received considerable attention in the press •Concerns of an approaching polarity reversal
•The magnetic field protects Earth’s surface from high-energy particles•Sun wind, cosmic rays from deep space
•When the field switches polarity, its strength can drop to below 10%• for few 1000 years.•with potentially disastrous consequences for: the atmosphere, the
climate and life.
•These concerns are supported by observational facts
55 The approaching polarity reversal The approaching polarity reversal
Date/Period Dipole moment
In 2005 7.776 x 1022 A m2
In 2000 7.779 x 1022 A m2
Over the last 800.000 years 7.5 ± 1.7 x 1022 A m2
Over 0.8-1.2 million years 5.3 ± 1.5 x 1022 A m2
•The first term of the spherical harmonic expansion •It can be recovered in the past (paleomagnetic records)
•Measurements show rapid and steady decrease of the geomagnetic dipole moment
•Primary motive for pondering the possibility of an approaching reversal
•The geomagnetic field amplitude is a fluctuating quantity
• The present dipole moment is still significantly higher than its averaged value •Over the last polarity interval and the three preceding ones
The dipole moment:
55 The approaching polarity reversal The approaching polarity reversal
•Tilt angle according to the axis of rotation
•The angle is rapidly increasing toward 90°
•Opposite of what is expected for a reversal
Direction of the dipole moment:
55 The approaching polarity reversal The approaching polarity reversal
The magnetic dip poles: NorthNorth SouthSouth
2000
1960
1980
•The two places on Earth
•Horizontal component of the field is zero
•Local objects
•They are affected by all components in a spectral expansion
•Move independently of one another
•The northern magnetic dip pole velocity 40 km/year ( last few years)15 km/year (last century)
•The southern magnetic dip pole velocitydecreasing (now 10 km/year)
•The dip pole is simply an ill defined quantity
55 The approaching polarity reversal The approaching polarity reversal
•The last reversal dates back some 800.000 years
•7 reversal in last 2 million years
•The reversal rate is not constant
•Average over few million years is 1 per million years•Maximum value is 6 reversals per million years•Maximum: Superchrones (10 millions years)
The overdue reversal:
6 6 ConclusionsConclusions
•Numerical models are successful but: restricted to a very remote parameter regime viscous force is much larger than are in the liquid core
•Experimental fluid dynamos were created (1999 in Latvia and Germany) the flows were extremely confined
•Dynamo action works on a large variety of natural bodies planets in the solar system (Venus and Mars excepted) Sun (reverses with a relatively regular period of 22 years) galaxies exhibit their own large-scale magnetic field
•Evidence for an imminent reversal remains rather weak•The typical timescale for a reversal is of the order of 1000 years
Thank youThank you