Comparison of 2D and 3D compressible convection in a pre-main sequence star

Context. A 1D description of stellar dynamics is at the basis of stellar evolution modeling. Designed to investigate open problems in stellar evolution, the MUltidimensional Stellar Implicit Code expands a realistic 1D profile of a star's internal structure to examine the interior dynamics of a specific star through either 2D or 3D hydrodynamic simulations.Aims. Extending our recent studies of 2D stellar convection to 3D stellar convection, we aim to compare 3D hydrodynamic simulations to identically set-up 2D simulations, for a realistic pre-main sequence star.Methods. We compare statistical quantities related to convective flows including: average velocity, vorticity, local enstrophy, and penetration depth beneath a convection zone. These statistics were produced during stationary, steady-state compressible convection in the star's convection zone.Results. Our simulations confirm the common result that 2D simulations of stellar convection have a higher magnitude of velocity on average than 3D simulations. Boundary conditions and the extent of the spherical shell can affect the magnitude and variability of convective velocities. The difference between 2D and 3D velocities is dependent on these background points; in our simulations this can have an effect as large as the difference resulting from the dimensionality of the simulation. Nevertheless, radial velocities near the convective boundary are comparable in our 2D and 3D simulations. The average local enstrophy of the flow is lower for 2D simulations than for 3D simulations, indicating a different shape and structuring of 3D stellar convection. We performed a statistical analysis of the depth of convective penetration below the convection zone using the model proposed in our recent study (Pratt et al. 2017, A&A, 604, A125). That statistical model was developed based on 2D simulations, which allowed us to examine longer times and higher radial resolution than are possible in 3D. Here, we analyze the convective penetration in 3D simulations, and compare the results to identically set-up 2D simulations. In 3D simulations, the penetration depth is as large as the penetration depth calculated from 2D simulations.