Supergranule Scale Convection Simulations Robert Stein, David Benson, Dali Georgobiani Michigan State University, USA Aake Nordlund, Copenhagen University, DK

Supergranulation Simulation 48 Mm wide x 20 Mm deep 65 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 Temperature, Density and Pressure (K) (105 dynes/cm2) (10-7 gm/cm2)

Mean Atmosphere Ionization of He, He I and He II

Surface Shear Layer f-plane rotation latitude of 30 degrees imposed rotation through the coriolis force --- not an imposed profile +/- signs --- directions ???? plot is an hour average --- after how long? -- recent ---> just beginning to study this significant fluctuations -- particularly near the surface extent is larger than observed --- likely due to the viscous flux in the numerical viscosity

Velocity in vertical plane -- 6.5 hr sequence (out of 50 hrs). single slice -- 48Mm by 20 Mm deep downflows merge and swept to sides by the diverging upflows some are merging -- some are getting halted by colliding with upflows in total ---> 46 hours solar -- 1 turnover time --- here 6 hours

vertical velocity on horizontal planes (48 Mm wide) l to r --> top to bottom surface, 2, 4, 8, 12, 16 Mm scale of features gradually (continually) gets larger with depth note: bottom has not relaxed yet no special thing for mesogranulation -- no special thing for supergranulation -- why so apparent is still not clear l to r --> top to bottom :: surface, 2Mm, 4Mm, 8Mm, 12Mm, 16Mm Continuous scale change: granulates -> supergranules

Scan of temperature with depth

Time evolution at various depths

How to calculate the spectrum? Average power spectra (correct) or Average time sequence (incorrect) Noisy Artificial feature,

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

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

Horizontal Velocity Spectrum -200 km 0 Mm 2 Mm 4 Mm 8 Mm 16 Mm

Upflows at surface come from small area at bottom (left) Downflows at surface converge to supergranule boundaries (right) seeded at regular intervals at bottom --- 1 Mm intervals upflows -- most turns over before it gets to the surface most of the upflows diverging -- see them coming back down at the edges of the supergranules color -- just shading -- yellow at bottom and red at top catch basin for the downflows merging of downflows thanks to Chris Henze at NASA Ames

Stream lines seeded at bottom

Wave propagation Courtesy Junwei Zhao

k-w Diagram simulation MDI

Time-Distance Inversions Depth 1-2 Mm Simulation Inversion Time-Distance Inversions Depth 1-2 Mm

Time-Distance Inversions Depth 2-3 Mm Simulation Inversion Time-Distance Inversions Depth 2-3 Mm

Time-Distance Inversions Depth 4-5 Mm Simulation Inversion Time-Distance Inversions Depth 4-5 Mm

Initialization Snapshot Doubled + Stretched = bootstraped initial state Snapshots of methods + composite (?)