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Numerical Simulations of Supergranulation and
Solar Oscillations
Åke Nordlund
Niels Bohr Institute, Univ. of Copenhagen
with
Bob Stein (MSU)
David Benson, Dali Georgobiani
Sasha Kosovichev, Junwei Zhao (Stanford)
Experiment settings: Code
Staggered mesh code conservative, with radiative transfer
fast – about 5 CPU-microseconds / mesh-update includes 4-bin radiative transfer
massively parallel OpenMP up to about 250 CPUs MPI up to thousands of CPUs (just developed) Hybrid MPI/OMP for clusters with shared mem. nodes
e.g. DCSC/KU: 118 nodes x dual-CPUs x dual core AMD = 472 cores (corresponds to ~90 million zone-updates / sec)
Stagger Code:Scaling on Columbia (Altix)
With OpenMP
With MPI
Size N-cpu µsec/pnt
125x500x125 1 5.9
250x500x250 64 8.6
500x500x500 64 7.8
500x500x500 125 9.3
500x500x500 250 11.9
Size N-cpu µsec/pnt
250x500x250 1 4.3
250x500x250 50 4.7
500x500x500 50 5.3
500x500x500 100 6.1
500x500x500 250 6.7
Supergranulation Simulation48 Mm wide x 20 Mm deep
63 hours (1.3 turnover time) f-plane rotation (surface shear layer) No magnetic field (yet) Low resolution:
• 100 km horizontal, • 12-70 km vertical
Mean Atmosphere: Ionization of Hydrogen and Helium
What can we learn?
Use the model and data as a test bed SOHO/MDI synthetic data
what does SOHO/MDI actually measure, and how well? Local helioseismology
what do the various methods measure, and how well?
Nature of the flow field What is ‘supergranulation’? How does it fit in with larger & smaller scales?
Data sets available onStanford Helioseismology Archive
Upflows at surface come from small area at bottom (left)Downflows at surface converge to supergranule boundaries (right)
Animation
Time evolution at various depths
Velocity at the same depths
The solar velocity spectrum
Power spectra are often plotted log-log, which means the power per unit x-axis is really k P(k), rather than just P(k)!
Solar velocity spectrum
MDI doppler (Hathaway) TRACE
correlation tracking (Shine)
MDI correlation tracking (Shine)
3-D simulations (Stein & Nordlund)
V ~ k
V~k-1/3
constantV
Velocity spectrum:
v(k) = (k P(k))1/2
Rotation subtracted solar Doppler image
Ni 6768 response function
simulation MDI
k- Diagram
Sub-sonic filtering
~ 7 km/s~ 7 km/s
P-mode power (red), convective power (black) – time average (blue)
Hi-res MDI
Note that it matters very much how one
computes power spectra
Velocity spectrumonly distinct scale is granulation
Vhoriz (sim)
Vz(sim)
V MDI
- - - - convection
…. oscillations
A continuous solar velocity spectrum!
Supergranulation may stand out a little
But the flow is nearly scale-invariant amplitudes scale inversely with size lifetimes scale with the square of the size
A Nearly Scale Free Spectrum!Doppler Image of the Sun (SOHO/MDI)
Solar horizontal velocity (observed)Scales differ by factor 2 – which is which?
400 Mm
200 Mm
100 Mm
50 Mm
Solar horizontal velocity (model)Scales differ by factor 2 – which is which?
24 Mm12 Mm
6 Mm3 Mm
Solar velocity spectrum
Time-Distance Diagram
f-mode Travel Times vs Simulated Flow Fields (divergence)
Right side image shows the f-mode outgoing and ingoing travel time differences, and the left side image shows the divergence computed from simulation. (From Junwei Zhao)
f-mode Travel Times vs Simulated Flow Fields (Horizontal)
Right side image shows the f-mode north-going and south-going travel time differences, and the left side image shows the Vn-s
averaged from simulation. (From Junwei Zhao & Aaron Birch)
Local Correlation Tracking
Sunspots
Sunspot, initial time evolution
Sunspot, time evolution (rep.)
Temperature, hor. & vert. magn. field,hor. & vert. velocity, surface intensity
Velocity, as seen by VAPOR(top perspective)
Sunspot,log magnetic pressure
Sunspot, field lines with density iso-surface (~solar surface)
Field line detail
Key result: A continuous solar velocity spectrum
Supergranulation may stand out a little
But the flow is nearly scale-invariant amplitudes scale inversely with size lifetimes scale with the square of the size
Data sets available onStanford Helioseismology Archive
Experiments:Forthcoming
AR magnetic fields add B from MDI magnetogram (as in Gudiksen &
Nordlund)
Quiet Sun magnetic fields advect initially horizontal field from the bottom b.c.
Rise of magnetic flux tube Insert flux tube near bottom, study emergence through
surface
Coronal & chromospheric heating similar to Gudiksen & Nordlund, but “real driving”
The End The End