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Turbulent Convection in Stars Kwing Lam Chan Hong Kong University of Science and Technology
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Turbulent Convection in Stars
Kwing Lam ChanHong Kong University of Science and Technology
“A Birthday Celebration of the Contribution of Bernard Jones to our
Understanding of the Universe”
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Relevance of Stellar Convection
Many unsolved problems and uncertainties in stellar astrophysics are related to convection.
e.g. massive star evolution, calibration of cluster age, …
The mixing length approach is still being heavily used.
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Nature of Stellar Convection and Difficulties
• Strong Nonlinearity - Turbulence• Deeply stratified - Large dynamical ranges
e.g. in the solar case:
depth of convection zone/ Kolmogorov micro scale ~ 10 12
thermal relaxation time/ eddy turnover time ~ 10 6 yr / 10min ~ 10 11 (limit the problem)
sound speed/ fluid velocity ~ 10 4 (implicit approach)
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Two Types of Numerical Approaches
• Numerical Experiments - to study principles relaxation enforced (i) Direct Numerical Simulations (ii) Large Eddy Simulations for Re>>1
relevance based on ‘similarity’
• Realistic Simulations - to match observations
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An Example of Numerical Experiments- Testing the Mixing Length Theory
An update (270x270x100 grids) of Chan & Sofia’s 1987 calculation (28x28x46 grids)
Horizontal cuts at different depths of the vertical velocity field and the temperature field for deep convection (8.5 pressure scale heights) in a 6x6x1 box
Bottom level Top level
Vz
T
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Turbulence Spectrum and Comparison with MLT Formulas
-5/3 line (V/CS)2
T”/T
An update (270x270x100 grids) of Chan & Sofia’s 1996 calculation (69x69x100 grids)
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An Example of Realistic Simulations- Solar Granulation
Stein & Nordlund (1989) An update (6Mmx6Mmx2.2Mm, 174x174x86 grids) of Kim & Chan’s 1998 calculation (1.2Mmx1.2Mmx1.5Mm, 58x58x60 grids)
< vertical cut of temperature field
< horizontal cut of temperature field
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Elimination of Micro-turbulence in Spectral Line Formation
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Extension to Other Stars
A simulation of Procyon’s granulation by Robinson et al. 2005
29Mmx29Mmx16.3Mm142x142x160 grids
A horizontal cut of the vertical velocity field
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Current Interest- Rotating Convection
A 6x6x1 box(378x378x80 grids)at 22.5o latitude
Coriolis number= L/V ~ 9
Longitude
Latitude
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Faster Spinning – Cyclones and Anticyclones
L/V ~ 18 L/V ~ 36
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AGAIN, HAPPY BIRTHDAY
BERNARD
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Simulation of Magnetic Loop Over an Active Region
A. Nordlund (2003)- Convective wiggling creates million degree Corona