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Solar Turbulence

Solar Turbulence. Friedrich Busse Dali Georgobiani Nagi Mansour Mark Miesch Aake Nordlund Mike Rogers Robert Stein Alan Wray. Solar Dynamics is driven by Turbulent Convection. Convection transports energy toward the surface through the outer 1/3 of the Sun.

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Solar Turbulence

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  1. Solar Turbulence Friedrich Busse Dali Georgobiani Nagi Mansour Mark Miesch Aake Nordlund Mike Rogers Robert Stein Alan Wray

  2. Solar Dynamicsis driven byTurbulent Convection

  3. Convection transports energy toward the surface through the outer 1/3 of the Sun

  4. Convection produces magnetic fields by dynamo action Courtesy M. DeRosa

  5. Convection generates waves by Reynolds stress & entropy fluctuations

  6. Waves probe the solar interior

  7. Magnetic fields control the behavior of the solar atmosphere

  8. Magnetic fields control the Sun-Earth interaction

  9. We therefore Model Solar Turbulent Magneto-Convection • Solve the equations of mass, momentum & energy conservation + induction equation • Model both deep & surface regions of the convection zone [Time scale too disparate to model jointly]

  10. Global Modeling:spherical simulations of deep convection zone

  11. Boundary Sensitivities A B C • A: Stable zone below convective envelope • B: “control” • C: Larger entropy gradient at the upper boundary Convection structure appears similar, has narrower & more homogeneous downflow network in case C

  12. Boundary Sensitivities (cont.) B C A both convective overshoot & more vigorous driving at top reduces angular velocity gradients!

  13. Acoustic Wave Propagation Solve linearized equations in background state Unperturbed Gaussian bump in T Will be used to develop improved methods for helioseismic imaging of structures below the surface or on the far-side of the sun

  14. Surface Convection:Boundary Sensitivities - horizontal field

  15. Boundary Sensitivities - vertical field

  16. Radiation drives solar convection & determines what we observe Test radiative solution algorithms to improve simulations Questions to be addressed • Determine angular resolution for good accuracy and speed • Test possible improvements in the solvers: discretization, quadradures, binning, etc… • Develop moment models for computing the solar atmosphere • Estimate the anisotropy to test closures and stiffness • Calculate accurate radiative pressures to derive/test closure models • Determine the best frequency binning and averaging techniques

  17. Supergranulation scale convection:first relax 24x24x9 Mm, then 50x50x20 Mm • Origin of supergranulation • Role of HeII ionization • Role of magnetic field • Emergence of magnetic flux • Maintenance of magnetic network • Boundary condition for coronal heating simulations Vertical velocity

  18. 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 ~ scale free

  19. Scale Free Spectrum?Doppler Image of the SunMichelson Doppler Interferometer (SOHO/MDI)

  20. 400 Mm 100 Mm 50 Mm 200 Mm Solar horizontal velocity (observed)Scales differ by factor 2 – which is which?

  21. Solar velocity spectrum24 Mm simulation will fill gap

  22. Convection: Temporal Spectrumis function of spatial scale k=3 k=9 k=1

  23. Width & Power

  24. Onset of Magneto-Convection • Toy model: uniform twisted horizontal field, with direction a function of height only • Critical Rayleigh number, Ra = gabd4/nk, for onset(g=gravity, a=DT/d, b=thermal expansion, d=height, n=kinematic viscosity, k=thermal diffusivity) • Independent of the layer height if based on the local scale of convection • Inversely proportional to vertical scale of background field • Proportional to B2

  25. Convective Scale, @ onset L ~ (h/B)1/2 (rsn)1/4 if L small, independent of layer height h = height for 180 twist s = conductivity

  26. The End

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