Barut, a. o. electrodynamics and classical theory of fields and particles (dover, 1980)--
Mean-field electrodynamics → no local fields considered
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Transcript of Mean-field electrodynamics → no local fields considered
Cellular Dynamo in a RotatingCellular Dynamo in a RotatingSpherical ShellSpherical Shell
Alexander GetlingAlexander GetlingLomonosov Moscow State UniversityLomonosov Moscow State University
Moscow, RussiaMoscow, Russia
Radostin Simitev,Radostin Simitev, Friedrich Busse Friedrich Busse University of Bayreuth, GermanyUniversity of Bayreuth, Germany
The problem of solar The problem of solar dynamo:dynamo: interplay between interplay between
global and local magnetic fields global and local magnetic fields needs to be includedneeds to be included
Mean-field electrodynamics Mean-field electrodynamics →→ no local fieldsno local fields considered considered
Possible alternative Possible alternative →→ “ “deterministic” dynamo deterministic” dynamo with well-with well-defineddefined structural elements in the flow andstructural elements in the flow and magnetic fieldmagnetic field
Kinematic model of Kinematic model of cellular dynamocellular dynamo
(cell = toroidal eddy)(cell = toroidal eddy)::
A.V. Getling and B.A. Tverskoy, A.V. Getling and B.A. Tverskoy,
Geomagn. AeronGeomagn. Aeron. . 1111, 211, 389 , 211, 389
(1971)(1971)
Convective mechanism of Convective mechanism of magnetic-field amplification magnetic-field amplification
and structuring and structuring
This study is based onThis study is based on
numerical simulations of numerical simulations of cellular magnetoconvection in cellular magnetoconvection in
a rotating spherical shella rotating spherical shell
The problemThe problem
Spherical fluid shellSpherical fluid shell Stress-free, electrically insulating Stress-free, electrically insulating
boundaries with perfect heat conductivityboundaries with perfect heat conductivity Uniformly distributed internal heat Uniformly distributed internal heat
sourcessources Boussinesq approximationBoussinesq approximation A small quadratic term is present in theA small quadratic term is present in the
temperaturetemperature dependence of densitydependence of density
The geometry of the The geometry of the problemproblem
Static temperature profileStatic temperature profile
o
i2oi
12
0s
s2
,1
1
2
1
3,
1
2
0
r
rdTTT
c
q
rrT
c
qT
p
p
Physical parameters of the Physical parameters of the problemproblem
The case discussed hereThe case discussed here
Geometrical parameter: Geometrical parameter: ηη = = 00..66
Physical parameters: Physical parameters: RRi i = = 30003000, , RRee = = − −
60006000, , ττ = = 110, 0, PP = = 11, , PPmm==3030
Computational parameter: Computational parameter: mm = = 55
Static profiles of temperatureStatic profiles of temperatureand its gradientand its gradient
Pseudospectral code Pseudospectral code employed:employed:
F.H. F.H. Busse, Busse, E. E. Grote, Grote, and A. and A.
Tilgner,Tilgner, Stud. Geophys. Geod.Stud. Geophys. Geod.
4242, 211 (1998), 211 (1998)
Radial velocity at Radial velocity at rr == rrii ++ 0.50.5 dd
t = 98.73
Azimuthal velocity and Azimuthal velocity and meridional streamlinesmeridional streamlines
t = 98.73
Radial magnetic field at Radial magnetic field at rr == rroo ++
0.70.7 dd
t = 98.73 t = 101.73
Radial magnetic field at Radial magnetic field at rr == rroo
Azimuthal magnetic field and Azimuthal magnetic field and meridional field linesmeridional field lines
t = 95.73 t = 101.73
Variations in poloidal Variations in poloidal components components HH11
00 and and HH2200 at at r r = =
0.50.5
Variations in full magnetic Variations in full magnetic energyenergy
Variations in dipolar-field Variations in dipolar-field energyenergy
axisymm. pol.axisymm. tor.
asymm. pol.asymm. tor.
Thank you for your Thank you for your attentionattention