Convection Simulations

Robert Stein

Ake Nordlund

Dali Georgobiani

David Benson

Werner Schafenberger

Objectives

• Understand supergranulation & the magnetic network

• Find signatures of emerging magnetic flux

• Validate and refine local helioseismic methods

Competed Simulations

• Hydrodynamic solar surface convection 96 Mm wide x 20 Mm deepDuration: 20.9 hours (bootstrapped from 48 Mm wide)Resolution: 100 km horizontal, 12-75 km vertical

• 48 Mm wide x 20 Mm deepDuration: 60 hours (boostrapped from 24 Mm wide)Resolution: 100 km horizontal, 12-75 km vertical

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

Computational Domain

20 M

m

Computational Domain for the CFD Simulations of Solar Convection

96 Mm

96 Mm

Mean AtmosphereTemperature, Density and Pressure

(105 dynes/cm2)

(10-7 gm/cm2)

(K)

Mean AtmosphereIonization of He, He I and He II

Energy Fluxes

Entropy Histogram

rms Velocity

rms Velocity, O-burning convection

Vertical

Horizontal

Courtesy Dave Arnett

Fractional area in Upflows

Fractional area in Upflows, O burningCourtesy Dave Arnett

Surface shear layerf-plane rotation

Vertical velocity: scan from

temperature minimum to 20 Mm

depth

size of cellular

structures increases with depth

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Streamlines: red down, blue up;15 hours; 48 x 20 Mm, vertical scale is depth

some downflows are halted, others merge into larger structures

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Tracer particles: 48 x 20 Mm, 15 hours, vertical scale is grid not depth

(white is fastest, dark is slowest)

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Velocity spectrum

Horizontal Velocity Spectrum

0 Mm

2 Mm4 Mm8 Mm

16 Mm

-200 km

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

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

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Streamlinesseeded

at bottom

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Streamlines:red=downblue=

up.Seededin the

middle

Mass Conservation

Rising fluidmust turn over and descend

within about ascale height toconserve mass.

The actualmixing

(entrainment) length in the simulation is

1.8 HP.

Vorticity:

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)

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Energy balancebuoyancy work ~ dissipation

(~ div FKE @ surface)

Buoyancy work,

O-burning driven

convection

courtesyD. Arnett

Dissipation length ~ 4 HP

KE, FKE, div FKE

Wave generation & propagation

Courtesy Junwei Zhao

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simulation MDIk- Diagram

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

6x6x3 Mmstreamlines seeded near bottom

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6x6x3 Mmfieldines seeded near bottom

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Vertical velocity (image) (km/s) & Velocity vectors

in slice

Vertical velocity (image) (km/s) & Magnetic field lines

in slice

Temperature (image) &Velocity vectors

in slice

The End