Turbulent convection in stellar interiors. I. Hydrodynamic simulation

We describe the results of 3D numerical simulations of oxygen shell burning and hydrogen core burning in a 23 M_⊙ stellar model. A detailed comparison is made to stellar mixing-length theory (MLT) for the shell-burning model. Simulations in 2D are significantly different from 3D, in terms of both 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 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 upflows and downflows, 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 that induce mixing through a 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 and simulation and observation of terrestrial atmospheric mixing. In particular, the normalized entrainment rate E = u_E/σH is well described by a power-law dependence on the bulk Richardson number Ri_B = ΔbL/ σ²_H for the conditions studied, 20 ≲ Ri _B ≲ 420. We find E = ARi^-n_B, with best-fit values log,A = 0.027 ±0.38 and n = 1.05 ±0.21. We discuss the applicability of these results to stellar evolution calculations.