Origin of Geomagnet

1.Introduction to MHD2.Dynamo theory

3.Geodynamo3.5 Secular variation&Field reversals

4.Reference

김희준

Magnetohydrodynamics

Fluid Mo-tion

Mag-netic fields

Fundamental eqs.

• Maxwell’s eqs. (→continuity eq)• Navier-Stokes eq.• Ohm’s law• Incompressible flow

Del dot u=0

div

MHD approximation

• E is gone!• Induction equation– cf)vorticity eq

Magnetic Reynolds Number

• Non-dimensionalisation of induction eq.

• Measures relative strength• Two limiting cases

Diffusive limit Rm<<1

L 3000km sigma 3x10^5

Field is not decaying!!

Perfectly conducting limit Rm>>1

Alfven’s theorem:

The magnetic flux through any material sur-face of a perfectly con-ducting fluidis a constant.

Lorentz Force

• Magnetic pressure• Magnetic tension

Dynamo theory

1. Can we construct a steady velocity field leading to dynamo action? yes

2. Can the velocity field be maintained by some force, say Coriolis or buoy-ancy force, in the face of lorentz force which tends to slow the fluid down? maybe

=>no self-consistent model of geo- dynamo yet!

Energetics

Antidynamo theory

• Cowling’s theorem

Mean-field dynamo theory

Re-call-cowl-ing’s the-orem

Geodynamo

Azimuthal&poloidal field inducing each

other

Differential rotation

Small-scale turbu-lance

α -ω model

• Differential rotation: • A- effect:

α -effect

Differential ro-tationα -effect: possibility

for α^2 dynamo

Axisymmetric field decomposi-tion

Axisymmetric mean field dynamo

Decaying of poloidal field

Secular variation & Field reversals

• Secular variation is thought to be caused by outer part of the core moving slower than the inner part.

• Convection!• Free-decay models vs Dynamic-re-

versing models• Deterministic chaotic vs nonchaotic

Reference

Davidson, An introduction to Magneto-hydrodynamicsMerrill, Mcelhinny, Mcfadden, The Magnetic Field of The Earth

http://www.maths.gla.ac.uk/~drf/courses/mhd/lect1.pdf