Gary A Glatzmaier

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Direct simulation of planetary and stellar
dynamos I. Methods and results
Gary A Glatzmaier University of California, Santa
Cruz
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Ra (convective driving) /
(viscous and thermal diffusion)
Ek (viscous diffusion) / (Coriolis effects)
Pr (viscous diffusion) /
(thermal diffusion) q
(thermal diffusion) / (magnetic diffusion)
Roc (Ra/Pr)1/2 Ek (convective
driving) / (Coriolis effects)
N/W if stable Re
(fluid velocity) / (viscous diffusion velocity)
Rm (fluid velocity) / (magnetic
diffusion velocity) Ro (fluid
velocity) / (rotational velocity)
Rom (Alfven velocity) / (rotational velocity)

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• Numerical method
• poloidal / toroidal decomposition of momentum
  density
• and magnetic field
• spherical harmonics and Chebyshev polynomials
• - spectral transform method, Chebyshev
  collocation and a semi-implicit time
  integration
• parallel (MPI)

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Radial velocity
Brun, Miesch, Toomre
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Enstrophy
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Radial magnetic field
Brun, Miesch, Toomre
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Toroidal magnetic field
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Poloidal magnetic field
Brun, Miesch, Toomre
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Dipole moment
Pole latitude
kyrs
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Entropy
In equatorial plane viewed
from northern hemisphere
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Kinetic energy
In equatorial plane viewed from
northern hemisphere
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Magnetic energy
In equatorial plane viewed from
northern hemisphere
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Longitudinal velocity
In equatorial plane viewed from
northern hemisphere
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Jupiter dynamo simulations
Longitudinal flow
Anelastic
shallow
deep
Glatzmaier
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Zonal winds
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Radial magnetic field
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Current 3D global MHD dynamo models for the
Earth, Jupiter and the sun
Many differences dimension, mass,
rotation rate, equation of state, heat
flux, force balance, energy balance,
differential rotation, magnetic reversals

Possible similarities in toroidal field
generation Earth _at_ ICB / tangent
cylinder Sun _at_ tachocline
Jupiter _at_ hydrogen phase transition
Model shortcomings low resolution
large diffusivities laminar flow
(Boussinesq)
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Challenges for the next generation of
global dynamo models
high spatial resolution in 3D small
diffusivities turbulent flow density
stratification gravity waves in stable
regions phase transitions
massively parallel computing improved numerical
methods anelastic equations sub-grid
scale models