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