mean-field electrodynamics → no local fields considered
DESCRIPTION
Cellular Dynamo in a Rotating Spherical Shell Alexander Getling Lomonosov Moscow State University Moscow, Russia Radostin Simitev, Friedrich Busse University of Bayreuth, Germany. The problem of solar dynamo: interplay between global and local magnetic fields needs to be included. - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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)
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Convective mechanism of Convective mechanism of magnetic-field amplification magnetic-field amplification
and structuring and structuring
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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
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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
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The geometry of the The geometry of the problemproblem
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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
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Physical parameters of the Physical parameters of the problemproblem
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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
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Static profiles of temperatureStatic profiles of temperatureand its gradientand its gradient
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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)
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Radial velocity at Radial velocity at rr == rrii ++ 0.50.5 dd
t = 98.73
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Azimuthal velocity and Azimuthal velocity and meridional streamlinesmeridional streamlines
t = 98.73
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Radial magnetic field at Radial magnetic field at rr == rroo ++
0.70.7 dd
t = 98.73 t = 101.73
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Radial magnetic field at Radial magnetic field at rr == rroo
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Azimuthal magnetic field and Azimuthal magnetic field and meridional field linesmeridional field lines
t = 95.73 t = 101.73
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Variations in poloidal Variations in poloidal components components HH11
00 and and HH2200 at at r r = =
0.50.5
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Variations in full magnetic Variations in full magnetic energyenergy
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Variations in dipolar-field Variations in dipolar-field energyenergy
axisymm. pol.axisymm. tor.
asymm. pol.asymm. tor.
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Thank you for your Thank you for your attentionattention