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

Courtesy M. DeRosa Convection produces magnetic fields by dynamo action

Convection generates waves by Reynolds stress & entropy fluctuations

Waves probe the solar interior

Magnetic fields control the behavior of the solar atmosphere

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

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 ABC

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

Unperturbed Acoustic Wave Propagation Solve linearized equations in background state 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

Surface Convection: Boundary Sensitivities - horizontal field

Boundary Sensitivities - vertical field

Fluid Parcels reaching the surface Radiate away their Energy and Entropy Z S E  Q 

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 horizontal velocity (model) Scales differ by factor 2 – which is which? 24 Mm12 Mm 6 Mm3 Mm

Solar velocity spectrum 24 Mm simulation will fill gap

Convection: Temporal Spectrum is function of spatial scale k=9 k=3 k=1

Width & Power

Flux Emergence & Disappearance Emerging flux Disappearing flux

Onset of Magneto-Convection Toy model: uniform twisted horizontal field, with direction a function of height only Critical Rayleigh number, R a = g  d 4 /  for onset  g=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 B 2

Convective onset L ~ (h/B) 1/2 (  ) 1/4 if L small, independent of layer height h = height for 180 twist  = conductivity

The End