Turbulent Convection in Stars

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Turbulent Convection in Stars

Kwing Lam Chan

Hong 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 29Mmx29Mmx16.3Mm 142x142x160 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

Figure

Updating...

References

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