Internal Wave Generation by Convection
In Lecoanet et al. (2015), I ran simulations of an experiment of convective generation of internal waves in water. Here is a visualization of the flow.
I also compared the waves produced in this simulation to waves produced in several "simulations of the simulation." The waves are accurately reproduced in a bulk Reynolds stress forcing model simulation, but not in an interface forcing model simulation. Louis-Alexandre Couston is leading further work on this problem, extending calculations to three-dimensions, investigating the effects of rotation and magnetic fields, and better understanding how the radiative-convective boundary effects wave generation.
Convective Overshoot
It has been proposed that convective overshoot could mix carbon fuel out of a carbon flame in super-asymptotic giant branch stars. If this occurs, the flame could stall, leading to a "hydrid carbon-oxygen-neon" white dwarf. I ran simulations of convective overshoot in Lecoanet et al. (2016). Here we plot the concentration of a passive tracer field representing the carbon fraction. The plot shows a vertical slice through our 3D simulation.
I found the horizontal average of this tracer field evolves according to a self-similar solution. Examining this self-similar solution allows us to infer a turbulent diffusivity due to convective overshoot into the stably stratified flame. We find that when extrapolated to astrophysical parameters, this turbulent diffusivity is too small to disrupt the carbon flame.