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Extending our recent studies of two-dimensional stellar convection to 3D, we compare three-dimensional hydrodynamic simulations to identically set-up two-dimensional simulations, for a realistic pre-main sequence star. We compare statistical quantities related to convective flows including: average velocity, vorticity, local enstrophy, and penetration depth beneath a convection zone. These statistics are produced during stationary, steady-state compressible convection in the stars convection zone. Our simulations with the MUSIC code confirm the common result that two-dimensional simulations of stellar convection have a higher magnitude of velocity on average than three-dimensional 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 two-dimensional simulations than for three-dimensional simulations, indicating a different shape and structuring of 3D stellar convection. We perform 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). Here we analyze the convective penetration in three dimensional simulations, and compare the results to identically set-up 2D simulations. In 3D the penetration depth is as large as the penetration depth calculated from 2D simulations.
We examine a penetration layer formed between a central radiative zone and a large convection zone in the deep interior of a young low-mass star. Using the Multidimensional Stellar Implicit Code (MUSIC) to simulate two-dimensional compressible stella
Context: We study the impact of two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from a one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone r
Context. Recent, nonlinear simulations of wave generation and propagation in full-star models have been carried out in the anelastic approximation using spectral methods. Although it makes long time steps possible, this approach excludes the physics
(abridged) Context: The ratio of kinematic viscosity to thermal diffusivity, the Prandtl number, is much smaller than unity in stellar convection zones. Aims: To study the statistics of convective flows and energy transport as functions of the Prandt
The classic Lorenz equations were originally derived from the two-dimensional Rayleigh-Benard convection system considering an idealised case with the lowest order of harmonics. Although the low-order Lorenz equations have traditionally served as a m