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 \sim 1.1 H _ { p } 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= u _ { E } / \sigma _ { H } , is well described by a power law dependance on the bulk Richardson number Ri _ { B } = \Delta bL / \sigma _ { H } ^ { 2 } for the conditions studied , 20 \lesssim Ri _ { B } \lesssim 420 .
We find E = ARi _ { B } ^ { - n } , with best fit values , \log A = 0.027 \pm 0.38 , and n = 1.05 \pm 0.21 .
We discuss the applicability of these results to stellar evolution calculations .