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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. Staggered mesh code

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Numerical Simulations of Supergranulation and Solar Oscillations

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  1. 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)

  2. 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)

  3. Stagger Code:Scaling on Columbia (Altix) • With OpenMP • With MPI

  4. 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

  5. Mean Atmosphere: Ionization of Hydrogen and Helium

  6. 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?

  7. Data sets available onStanford Helioseismology Archive

  8. Upflows at surface come from small area at bottom (left)Downflows at surface converge to supergranule boundaries (right)

  9. Animation

  10. Time evolution at various depths

  11. Velocity at the same depths

  12. 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)!

  13. 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

  14. Rotation subtracted solar Doppler image

  15. Ni 6768 response function

  16. k-w Diagram simulation MDI

  17. Sub-sonic filtering ~ 7 km/s

  18. P-mode power (red), convective power (black) – time average (blue) Note that it matters very much how one computes power spectra Hi-res MDI

  19. Velocity spectrumonly distinct scale is granulation - - - - convection Vhoriz (sim) …. oscillations Vz(sim) V MDI

  20. 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

  21. A Nearly Scale Free Spectrum!Doppler Image of the Sun(SOHO/MDI)

  22. 400 Mm 100 Mm 50 Mm 200 Mm Solar horizontal velocity (observed)Scales differ by factor 2 – which is which?

  23. Solar horizontal velocity (model)Scales differ by factor 2 – which is which? 12 Mm 24 Mm 3 Mm 6 Mm

  24. Solar velocity spectrum

  25. Time-Distance Diagram

  26. 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)

  27. 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-saveraged from simulation. (From Junwei Zhao & Aaron Birch)

  28. Local Correlation Tracking

  29. Sunspots

  30. Sunspot, initial time evolution

  31. Sunspot, time evolution (rep.)

  32. Temperature, hor. & vert. magn. field,hor. & vert. velocity, surface intensity

  33. Velocity, as seen by VAPOR(top perspective)

  34. Sunspot,log magnetic pressure

  35. Sunspot, field lines with density iso-surface (~solar surface)

  36. Field line detail

  37. 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

  38. Data sets available onStanford Helioseismology Archive

  39. 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”

  40. TheEnd

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