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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 levelTop level VzVz T

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Turbulence Spectrum and Comparison with MLT Formulas -5/3 line (V/C S ) 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 22.5 o 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

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Interesting News… Regulus Age: a few hundred million years Mass: 3.5 solar masses Rotation Period: <1 day Equatorial Velocity: 200 km s -1 Axial tilt:

Interesting News… Regulus Age: a few hundred million years Mass: 3.5 solar masses Rotation Period: <1 day Equatorial Velocity: 200 km s -1 Axial tilt:

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