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Our ability to predict the structure and evolution of stars is in part limited by complex, 3D hydrodynamic processes such as convective boundary mixing. Hydrodynamic simulations help us understand the dynamics of stellar convection and convective boundaries. However, the codes used to compute such simulations are usually tested on extremely simple problems and the reliability and reproducibility of their predictions for turbulent flows is unclear. We define a test problem involving turbulent convection in a plane-parallel box, which leads to mass entrainment from, and internal-wave generation in, a stably stratified layer. We compare the outputs from the codes FLASH , MUSIC , PPMSTAR , PROMPI , and SLH , which have been widely employed to study hydrodynamic problems in stellar interiors. The convection is dominated by the largest scales that fit into the simulation box. All time-averaged profiles of velocity components, fluctuation amplitudes, and fluxes of enthalpy and kinetic energy are within ≲3 σ of the mean of all simulations on a given grid (128 3 and 256 3 grid cells), where σ describes the statistical variation due to the flow’s time dependence. They also agree well with a 512 3 reference run. The 128 3 and 256 3 simulations agree within 9% and 4%, respectively, on the total mass entrained into the convective layer. The entrainment rate appears to be set by the amount of energy that can be converted to work in our setup and details of the small-scale flows in the boundary layer seem to be largely irrelevant. Our results lend credence to hydrodynamic simulations of flows in stellar interiors. We provide in electronic form all outputs of our simulations as well as all information needed to reproduce or extend our study. 

In most songbirds, the processes of song learning and territory establishment overlap in the early life and a young bird usually winds up with songs matching those of his territorial neighbors in his first breeding season. In the present study, we examined the relationships among the timing of territory establishment, the pattern of song learning and territorial success in a sedentary population of song sparrows (Melospiza melodia). Males in this population tend to learn their songs from their neighbors and consequently they show high song sharing with neighbors and use these shared songs preferentially in interactions with them. Males also show significant variation in the timing of territory establishment, ranging from their natal summer to the next spring. Using a three‐year dataset, we found that the timing of territory establishment did not systematically affect the composition of the song repertoire of the tutee: early establishers and late establishers learned equally as much from their primary tutors and had a similar number of tutors and similar repertoire sizes, nor did timing of territory establishment affect subsequent survival on territory. Therefore, the song‐learning program of song sparrows seems versatile enough to lead to high song sharing even for birds that establish territories relatively late.