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