Convective boundary mixing is one of the major uncertainties in stellar evolution .
In order to study its dependence on boundary properties and turbulence strength in a controlled way , we computed a series of 3D hydrodynamical simulations of stellar convection during carbon burning with a varying boosting factor of the driving luminosity .
Our 3D implicit large eddy simulations were computed with the prompi code .
We performed a mean field analysis of the simulations within the Reynolds-averaged Navier-Stokes framework .
Both the vertical RMS velocity within the convective region and the bulk Richardson number of the boundaries are found to scale with the driving luminosity as expected from theory : v \propto L ^ { 1 / 3 } and Ri _ { \textrm { B } } \propto L ^ { -2 / 3 } , respectively .
The positions of the convective boundaries were estimated through the composition profiles across them , and the strength of convective boundary mixing was determined by analysing the boundaries within the framework of the entrainment law .
We find that the entrainment is approximately inversely proportional to the bulk Richardson number , Ri _ { \textrm { B } } ( \propto \textrm { Ri } _ { \textrm { B } } ^ { - \alpha } , \alpha \sim 0.75 ) .
Although the entrainment law does not encompass all the processes occurring at boundaries , our results support the use of the entrainment law to describe convective boundary mixing in 1D models , at least for the advanced phases .
The next steps and challenges ahead are also discussed .