3D Simulations and MLT. I. Renzini's Critique
Renzini wrote an influential critique of "overshooting" in mixing-length theory (MLT), as used in stellar evolution codes, and concluded that three-dimensional fluid dynamical simulations were needed. Such simulations are now well tested. Implicit large eddy simulations connect large-scale stellar flow to a turbulent cascade at the grid scale, and allow the simulation of turbulent boundary layers, with essentially no assumptions regarding flow except the number of computational cells. Buoyant driving balances turbulent dissipation for weak stratification, as in MLT, but with the dissipation length replacing the mixing length. The turbulent kinetic energy in our computational domain shows steady pulses after 30 turnovers, with no discernible diminution; these are caused by the necessary lag in turbulent dissipation behind acceleration. Interactions between coherent turbulent structures give multi-modal behavior, which drives intermittency and fluctuations. These cause mixing, which may justify use of the instability criterion of Schwarzschild rather than the Ledoux. Chaotic shear flow of turning material at convective boundaries causes instabilities that generate waves and sculpt the composition gradients and boundary layer structures. The flow is not anelastic; wave generation is necessary at boundaries. A self-consistent approach to boundary layers can remove the need for ad hoc procedures of "convective overshooting" and "semi-convection." In Paper II, we quantify the adequacy of our numerical resolution in a novel way, determine the length scale of dissipation—the "mixing length"—without astronomical calibration, quantify agreement with the four-fifths law of Kolmogorov for weak stratification, and deal with strong stratification. ; Theoretical Astrophysics Program (TAP) at the University of Arizona; Australian Research Council though the Future Fellowship grant entitled "Where Are the Convective Boundaries in Stars?" [FT160100046]; Australian Government; Government of Western Australia; National Science Foundation [OCI-1053575]; NASA [NNX16AB25G]; Office of Science of the U.S. Department of Energy [DEAC0205CH11231]; EUFP7ERC2012St Grant [306901]; World Premier International Research Centre Initiative (WPI Initiative), MEXT, Japan; COST (European Cooperation in Science and Technology) [CA16117]; Swiss National Science Foundation; Equal Opportunity Office of the University of Geneva; BEIS capital funding via STFC capital grants [ST/P002293/1, ST/R002371/1]; Durham University; STFC operations grant [ST/R000832/1]; BIS National E Infrastructure capital grant [ST/K00042X/1]; STFC capital grants [ST/H008519/1, ST/K00087X/1]; STFC DiRAC Operations grant [ST/K003267/1]; PRACE; Steward Observatory ; Open access article ; This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.