http://arxiv.org/abs/1810.04659
In a previous paper (Arnett, et al., 2019) we introduced the use of Reynolds averaged implicit large eddy simulations (Moc\’ak, et al., 2019) to the classical problem of stellar convection (B\”ohm-Vitense, 1958; mixing length theory, MLT). We explored the structure of turbulent boundary layers, multi-modal behavior, intermittency, fluctuations, and composition gradients, and found that the Kolmogorov dissipation length played a role in some respects akin to the B\”ohm-Vitense mixing length. We now extend our analysis by extracting the sub-grid dissipation of our method (the “mixing length”), and by quantifying errors in resolution of boundary layers. The results for weakly-stratified convection show quantitative agreement with the four-fifths law of Kolmogorov. We examine the differences between weakly and strongly stratified convection (i.e., core convection and surface convection zones, respectively). We find that MLT is a weak-stratification theory (which ignores turbulent kinetic energy), and for precise work should be modified for strong-stratification cases like the solar and stellar atmospheres. We derive the `effective mixing length’ for strong-stratification; it is the density scale height, so $\alpha \approx \Gamma \sim 5/3$, in surprising agreement with many stellar evolution calibrations, but smaller than the preferred values for the Standard Solar Model (SSM), an error we attribute in part to the lack of a turbulent boundary layer, which we find at the bottom of the convection zone but missing in MLT and SSM.
W. Arnett, C. Meakin, R. Hirschi, et. al.
Thu, 11 Oct 18
61/72
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