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Numerical Simulations of Supergranulation and Solar Oscillations PowerPoint Presentation

Numerical Simulations of Supergranulation and Solar Oscillations

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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

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

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?

- SOHO/MDI synthetic data
- 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)

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)!

3-D simulations (Stein & Nordlund)

V~k-1/3

MDI correlation tracking (Shine)

MDI doppler (Hathaway)

TRACE correlation tracking (Shine)

V ~ k

Solar velocity spectrumVelocity spectrum:

v(k) = (k P(k))1/2

Sub-sonic filtering

~ 7 km/s

P-mode power (red), convective power (black) – time average (blue)

Note that it matters very much how one computes power spectra

Hi-res MDI

Velocity spectrum average (blue)only distinct scale is granulation

- - - - convection

Vhoriz (sim)

…. oscillations

Vz(sim)

V MDI

A continuous solar velocity spectrum! average (blue)

- 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! average (blue)Doppler Image of the Sun(SOHO/MDI)

400 Mm average (blue)

100 Mm

50 Mm

200 Mm

Solar horizontal velocity (observed)Scales differ by factor 2 – which is which?Solar horizontal velocity (model) average (blue)Scales differ by factor 2 – which is which?

12 Mm

24 Mm

3 Mm

6 Mm

Solar velocity spectrum average (blue)

Time-Distance Diagram average (blue)

f-mode Travel Times vs Simulated Flow Fields (divergence) average (blue)

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 average (blue)-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-saveraged from simulation.

(From Junwei Zhao & Aaron Birch)

Local Correlation Tracking average (blue)

Sunspots average (blue)

Sunspot, initial time evolution average (blue)

Sunspot, time evolution (rep.) average (blue)

Temperature, hor. & vert. magn. field, average (blue)hor. & vert. velocity, surface intensity

Velocity, as seen by VAPOR average (blue)(top perspective)

Sunspot, average (blue)log magnetic pressure

Sunspot, field lines with average (blue)density iso-surface (~solar surface)

Field line detail average (blue)

Key result: A continuous solar velocity spectrum average (blue)

- 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 on average (blue)Stanford Helioseismology Archive

Experiments: average (blue)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 average (blue)End

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