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In this paper, we investigate the upward overshooting by three-dimensionalnumerical simulations. We find that the above convectively stable zone can bepartitioned into three layers: the thermal adjustment layer (mixing bothentropy and material), the turbulent dissipation layer (mixing material but notentropy), and the thermal dissipation layer (mixing neither entropy normaterial). The turbulent dissipation layer is separated from the thermaladjustment layer and the thermal dissipation layer by the first and second zeropoints of the vertical velocity correlation. The simulation results are in goodagreement with the prediction of the one-dimensional turbulent Reynolds stressmodel. First, the layer structure is similar. Second, the upper boundary of thethermal adjustment layer is close to the peak of the magnitude of thetemperature perturbation. Third, the P\'eclet number at the upper boundary ofthe turbulent dissipation layer is close to 1. In addition, we have studied thescalings of the overshooting distance on the relative stability parameter $S$,the Prandtl number $\rm Pr$, and the P\'eclet 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 decreaseswith $\rm Pe$. Finally, we calculate the ratio of the thickness of theturbulent dissipation layer to that of the thermal adjustment layer. The ratioremains almost constant, with an approximate value of 2.4.

Upward Overshooting in Turbulent Compressible Convection. I.Effects of the relative stability parameter, the Prandtl number, and the P\'eclet number