## arXiv Analytics

### arXiv:1810.04653 [astro-ph.SR]AbstractReferencesReviewsResources

#### 3D Simulations and MLT: I. Renzini's Critique

Published 2018-10-10Version 1

Renzini (1987) wrote an influential critique of mixing-length theory (MLT) as used in stellar evolution codes, and concluded that three-dimensional (3D) fluid dynamical simulations were needed to clarify several important issues. We have critically explored the limitations of the numerical methods and conclude that they are approaching the required accuracy. Implicit large eddy simulations (ILES) automatically connect large scale turbulence to a Kolmogorov cascade below the grid scale, allowing turbulent boundary layers to remove singularities that appear in the theory. Interactions between coherent structures give multi-modal behavior, driving intermittency and fluctuations. Reynolds averaging (RA) allows us to abstract the essential features of this dynamical behavior of boundaries which are appropriate to stellar evolution, and consider how they relate static boundary conditions (Richardson, Schwarzschild or Ledoux). We clarify several questions concerning when and why MLT works, and does not work, using both analytical theory and 3D high resolution numerical simulations. The composition gradients and boundary layer structure which are produced by our simulations suggest a self-consistent approach to boundary layers, removing the need for ad hoc procedures for 'convective overshooting' and semi-convection'. In a companion paper we quantify the adequacy of our numerical resolution, determine of the length scale of dissipation (the mixing length') without astronomical calibration, quantify agreement with the four-fifths law of Kolmogorov for weak stratification, and extend MLT to deal with strong stratification.

Categories: astro-ph.SR
Related articles: Most relevant | Search more
arXiv:1702.06726 [astro-ph.SR] (Published 2017-02-22)
The Boundary Layer in compact binaries
arXiv:1603.01147 [astro-ph.SR] (Published 2016-03-03)
Stellar evolution in the outer Galaxy
arXiv:1509.05262 [astro-ph.SR] (Published 2015-09-17)
Trends of Stellar Entropy along Stellar Evolution