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

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Origin of Geomagnet

Origin of Geomagnet1.Introduction to MHD2.Dynamo theory3.Geodynamo3.5 Secular variation&Field reversals4.Reference1MagnetohydrodynamicsFundamental eqs.Maxwells eqs. (continuity eq)Navier-Stokes eq.Ohms lawIncompressible flow

Del dot u=0

div

MHD approximationE is gone!Induction equationcf)vorticity eq

Magnetic Reynolds NumberNon-dimensionalisation of induction eq.Measures relative strengthTwo limiting cases

Diffusive limit Rm1

Alfvens theorem:The magnetic flux through any material surface of a perfectly conducting fluidis a constant.Lorentz ForceMagnetic pressureMagnetic tension

Dynamo theoryCan we construct a steady velocity field leading to dynamo action? yesCan 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 theoryCowlings theorem

Mean-field dynamo theory

Recallcowlings theoremPerturbation is relative to mean feld there.18Geodynamo - model

-effectDifferential rotation -effect: possibility for ^2 dynamoSmall scale random magnetic field is thought to organise it self in such a way as to reinforce the large scale dipole field. Ex)ferromagnetism20

Axisymmetric field decompositionAxisymmetric mean field dynamo

Decaying of poloidal field

Secular variation & Field reversalsSecular 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 modelsDeterministic chaotic vs nonchaotic

Free decay is not seemingly true.23ReferenceDavidson, An introduction to MagnetohydrodynamicsMerrill, Mcelhinny, Mcfadden, The Magnetic Field of The Earth

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

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