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In this paper, we investigate the upward overshooting by three-dimensional numerical simulations. We find that the above convectively stable zone can be partitioned into three layers: the thermal adjustment layer (mixing both entropy and material), the turbulent dissipation layer (mixing material but not entropy), and the thermal dissipation layer (mixing neither entropy nor material). The turbulent dissipation layer is separated from the thermal adjustment layer and the thermal dissipation layer by the first and second zero points of the vertical velocity correlation. The simulation results are in good agreement with the prediction of the one-dimensional turbulent Reynolds stress model. First, the layer structure is similar. Second, the upper boundary of the thermal adjustment layer is close to the peak of the magnitude of the temperature perturbation. Third, the Peclet number at the upper boundary of the turbulent dissipation layer is close to 1. In addition, we have studied the scalings of the overshooting distance on the relative stability parameter $S$, the Prandtl number $rm Pr$, and the Peclet number $rm Pe$. The scaling on $S$ is not unique. The trend is that the overshooting distance decreases with $S$. Fitting on $rm Pr$ shows that the overshooting distance increases with $rm Pr$. Fitting on $rm Pe$ shows that the overshooting distance decreases with $rm Pe$. Finally, we calculate the ratio of the thickness of the turbulent dissipation layer to that of the thermal adjustment layer. The ratio remains almost constant, with an approximate value of 2.4.
(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
(abridged) Context: Turbulent diffusion of large-scale flows and magnetic fields play major roles in many astrophysical systems. Aims: Our goal is to compute turbulent viscosity and magnetic diffusivity, relevant for diffusing large-scale flows and m
In this paper, we calibrate the coefficients for the one-dimensional Reynolds stress model with the data generated from the three-dimensional numerical simulations of upward overshooting in turbulent compressible convection. It has been found that th
Complex mixing and magnetic field generation occurs within stellar interiors particularly where there is a strong shear flow. To obtain a comprehensive understanding of these processes, it is necessary to study the complex dynamics of shear regions.
In this study, the stability dependence of turbulent Prandtl number ($Pr_t$) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functi