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Solar TurbulenceFriedrich 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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Courtesy M. DeRosa
Convection produces magnetic fields by dynamo action
Convection generates waves by Reynolds stress & entropy fluctuations
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Waves probe the solar interior
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Magnetic fields control the behavior of the solar atmosphere QuickTime™ and a
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Magnetic fields control the Sun-Earth interaction
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]
Global Modeling:spherical simulations of deep convection zone
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Boundary Sensitivities
• 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
A B C
Boundary Sensitivities (cont.)
both convective overshoot & more vigorous driving at top reduces angular velocity gradients!
BA C
Unperturbed
Acoustic Wave PropagationSolve linearized equations in background state
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Gaussian bump in T
Will be used to develop improved methodsfor helioseismic imaging of structures below the
surface or on the far-side of the sun
Surface Convection:Boundary Sensitivities - horizontal field
Boundary Sensitivities - vertical field
Radiation drives solar convection &determines what we observe
Test radiative solution algorithms to improve simulations
• 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
• Determine angular resolution for good accuracy and speed
• Test possible improvements in the solvers: discretization, quadradures, binning, etc…
Questions to be addressed
Supergranulation scale convection: first relax 24x24x9 Mm, then 50x50x20 Mm
Vertical velocity
•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
Solar velocity spectrum ~ scale free
MDI doppler (Hathaway) TRACE
correlation tracking (Shine)
MDI correlation tracking (Shine)
3-D simulations (Stein & Nordlund)
V ~ k
V~k-1/3
Scale Free Spectrum?Doppler Image of the Sun
Michelson Doppler Interferometer (SOHO/MDI)
Solar horizontal velocity (observed)Scales differ by factor 2 – which is which?
400 Mm
200 Mm
100 Mm
50 Mm
Solar velocity spectrum24 Mm simulation will fill gap
Convection: Temporal Spectrumis function of spatial scale
k=9
k=3
k=1
Width & Power
Onset of Magneto-Convection
• Toy model: uniform twisted horizontal field, with direction a function of height only
• Critical Rayleigh number, Ra = gd4/for onsetg=gravity, =T/d, =thermal expansion, d=height, =kinematic viscosity, =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
Convective Scale, @ onset
L ~ (h/B)1/2 ()1/4
if L small, independent of layer height
h = height for 180 twist
= conductivity
The End
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