Table A.1
Diffusion schemes applied in a few comparable studies.
| Study | Viscosity | Magnetic | Radiative | Mean entropy | Fluctuating entropy | |||||
| diffusivity | diffusion | diffusion | diffusion | |||||||
|
|
||||||||||
| Present work | ν | η | χ | χSGS | χSGS | |||||
| (Pencil Code) | (constant) | (constant) | (6.4 ×105× solar) | (piecewise constant) | (piecewise constant) | |||||
|
|
||||||||||
| Nelson et al. (2013), (ASH) | ν | η | κ r | κ 0 | κ | |||||
| Cases D3[a, b, pm1, pm2] | (∝ ρ− 1 / 2) | (∝ ρ− 1 / 2) | (solar) | (near surface) | (∝ ρ− 1 / 2) | |||||
|
|
||||||||||
| Nelson et al. (2013), | ν S | ηS ≡ νS/ Pm | κ r | κ 0 | κS ≡ νS/ Pr | |||||
| Case S3 | Smagorinsky | Smagorinsky | (solar) | (near surface) | Smagorinsky | |||||
|
|
||||||||||
| Ghizaru et al. (2010) | iLES | iLES | Newtonian | Newtonian | iLES+Newtonian | |||||
| (EULAG) | cooling | cooling | cooling | |||||||
|
|
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| Hotta et al. (2016) | ν | η | κ r | κ | κ | |||||
| Low | (∝ ρ− 1 / 2) | (∝ ρ− 1 / 2) | (solar) | (∝ ρ− 1 / 2) | (∝ ρ− 1 / 2) | |||||
|
|
||||||||||
| Hotta et al. (2016) | Slope-limited | Slope-limited | κ r | κ | κ | |||||
| Medium, High, High-S | diffusion | diffusivity | (solar) | (∝ ρ− 1 / 2) | (∝ ρ− 1 / 2) | |||||
Notes. The entries for each study correspond to the symbols used for the various diffusion coefficients and their spatial profiles or functional dependences, where applicable. The coefficients κr and κ0 are not mentioned by Nelson et al. (2013), who referred to an earlier study by Brown et al. (2010) for a detailed description of their model. iLES stands for implicit large-eddy simulation where the truncation errors of the numerical scheme provide the diffusion.
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