Origin of Geomagnet 1.Introduction to MHD 2.Dynamo theory 3.Geodynamo 3.5 Secular variation&Field reversals 4.Reference 김희준

Magnetohydrodynamics Fluid Motion Magnetic 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 Field is not decaying!!

Perfectly conducting limit Rm>>1 Alfven’s theorem: The magnetic flux through any material surface of a perfectly conducting fluid is 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 buoyancy 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 Recall cowli ng’s theor em

Geodynamo Azimuthal&poloidal field inducing each other Differential rotation Small-scale turbulance

α -ω model α -effect Differential rotation α -effect: possibility for α^2 dynamo

Axisymmetric field decomposition 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-reversing models Deterministic chaotic vs nonchaotic

Reference Davidson, An introduction to Magnetohydrodynamics Merrill, Mcelhinny, Mcfadden, The Magnetic Field of The Earth d/lect1.pdf