Turbulent Convection in Stellar Interiors. I. Hydrodynamic Simulation

We describe the results of three-dimensional (3D) numerical simulations designed to study turbulent convection in the stellar interiors, and compare them to stellar mixing-length theory (MLT). Simulations in 2D are significantly different from 3D, both in terms of flow morphology and velocity amplitude. Convective mixing regions are better predicted using a dynamic boundary condition based on the bulk Richardson number than by purely local, static criteria like Schwarzschild or Ledoux. MLT gives a good description of the velocity scale and temperature gradient for a mixing length of ∼ 1.1Hp for shell convection, however there are other important effects that it does not capture, mostly related to the dynamical motion of the boundaries between convective and nonconvective regions. There is asymmetry between up and down flows, so the net kinetic energy flux is not zero. The motion of convective boundaries is a source of gravity waves; this is a necessary consequence of the deceleration of convective plumes. Convective ”overshooting” is best described as an elastic response by the convective boundary, rather than ballistic penetration of the stable layers by turbulent eddies. The convective boundaries are rife with internal and interfacial wave motions, and a variety of instabilities arise which induce mixing through in process best described as turbulent entrainment. We find that the rate at which material entrainment proceeds at the boundaries is consistent with analogous laboratory experiments as well as simulation and observation of terrestrial atmospheric mixing. In particular, the normalized entrainment rate E=uE/σH , is well described by a power law dependance on the bulk Richardson number RiB = ∆bL/σ 2 H for the conditions studied, 20 . RiB . 420. We find E = ARi−n B , with best fit values, logA = 0.027 ± 0.38, and n = 1.05 ± 0.21. We discuss the applicability of these results to stellar evolution calculations. Subject headings: stars: evolution stars: nucleosynthesis massive stars hydrodynamics convection g-modes