1. Convection Simulations Robert Stein Ake Nordlund Dali Georgobiani David Benson Werner Schafenberger

2. Objectives Understand supergranulation & the magnetic network Find signatures of emerging magnetic flux Validate and refine local helioseismic methods

3. Competed Simulations Hydrodynamic solar surface convection 96 Mm wide x 20 Mm deep Duration: 20.9 hours (bootstrapped from 48 Mm wide) Resolution: 100 km horizontal, 12-75 km vertical 48 Mm wide x 20 Mm deep Duration: 60 hours (boostrapped from 24 Mm wide) Resolution: 100 km horizontal, 12-75 km vertical

4. Numerical Method Spatial differencing –6th-order f.d. –staggered Time advancement –3rd order Runga-Kutta Equation of state –tabular –including ionization –H, He + abundant elements Radiative transfer –3D, LTE –4 bin opacity distrib. fxn Quenching

5. Computational Domain 20 Mm Computational Domain for the CFD Simulations of Solar Convection 96 Mm

6. Mean Atmosphere Temperature, Density and Pressure (10 5 dynes/cm 2 ) (10 -7 gm/cm 2 ) (K)

7. Mean Atmosphere Ionization of He, He I and He II

8. Energy Fluxes

9. Entropy Histogram

10. rms Velocity

11. rms Velocity, O-burning convection Vertical Horizontal Courtesy Dave Arnett

12. Fractional area in Upflows

13. Fractional area in Upflows, O burning Courtesy Dave Arnett

14. Surface shear layer f-plane rotation

15. Vertical velocity: scan from temperature minimum to 20 Mm depth size of cellular structures increases with depth

16. Streamlines: red down, blue up;15 hours; 48 x 20 Mm, vertical scale is depth some downflows are halted, others merge into larger structures

17. Tracer particles: 48 x 20 Mm, 15 hours, vertical scale is grid not depth (white is fastest, dark is slowest)

19. Velocity spectrum

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

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

23. Stream lines seeded at bottom

24. Stream lines: red= down blue= up. Seeded in the middle

25. Mass Conservation Rising fluid must turn over and descend within about a scale height to conserve mass. The actual mixing (entrainment) length in the simulation is 1.8 H P.

26. Vortic ity: 11.75 hours, Finite Time Lyapunov Exponent Field, subdomain 21 Mm wide x 19 Mm high x 0.5 Mm thick, (from 48x 20 Mm simulation)

27. Energy balance buoyancy work ~ dissipation (~ div F KE @ surface)

28. Buoyancy work, O-burning driven convection courtesy D. Arnett

29. Dissipation length ~ 4 H P

30. KE, F KE, div F KE

31. Wave generation & propagation Courtesy Junwei Zhao

32. simulationMDI k-  Diagram

33. Horizontal velocity (2-3 Mm depth): simulation (left), travel time inversion (right)

34. 6x6x3 Mm streamlines seeded near bottom

35. 6x6x3 Mm fieldines seeded near bottom

36. Vertical velocity (image) (km/s) & Velocity vectors in slice

37. Vertical velocity (image) (km/s) & Magnetic field lines in slice

38. Temperature (image) & Velocity vectors in slice

39. The End