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

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Numerical simulations of supergranulation and solar oscillations

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
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
Stagger Code:Scaling on Columbia (Altix)

  • With OpenMP

  • With MPI


Supergranulation simulation 48 mm wide x 20 mm deep
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
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 on stanford helioseismology archive
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
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

3-D simulations (Stein & Nordlund)

V~k-1/3

MDI correlation tracking (Shine)

MDI doppler (Hathaway)

TRACE correlation tracking (Shine)

V ~ k

Solar velocity spectrum

Velocity spectrum:

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




K w diagram
k-w Diagram

simulation

MDI



P mode power red convective power black time average blue
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 only distinct scale is granulation
Velocity spectrum average (blue)only distinct scale is granulation

- - - - convection

Vhoriz (sim)

…. oscillations

Vz(sim)

V MDI


A continuous solar velocity spectrum
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 doppler image of the sun soho mdi
A Nearly Scale Free Spectrum! average (blue)Doppler Image of the Sun(SOHO/MDI)


Solar horizontal velocity observed scales differ by factor 2 which is which

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 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 spectrum1
Solar velocity spectrum average (blue)


Time distance diagram
Time-Distance Diagram average (blue)


F mode travel times vs simulated flow fields divergence
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 mode travel times vs simulated flow fields horizontal
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)



Sunspots
Sunspots average (blue)




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


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


Sunspot log magnetic pressure
Sunspot, average (blue)log magnetic pressure


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


Field line detail
Field line detail average (blue)


Key result a continuous solar velocity spectrum
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 stanford helioseismology archive1
Data sets available on average (blue)Stanford Helioseismology Archive


Experiments forthcoming
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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