3D Simulations and MLT. I. Renzini’s Critique

Abstract

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.