Upward Overshooting in Turbulent Compressible Convection. I.Effects of the relative stability parameter, the Prandtl number, and the P’eclet number. (arXiv:1911.06942v1 [astro-ph.SR])

Upward Overshooting in Turbulent Compressible Convection. I.Effects of the relative stability parameter, the Prandtl number, and the P’eclet number. (arXiv:1911.06942v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Cai_T/0/1/0/all/0/1">Tao Cai</a>

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 P’eclet 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 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 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.

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 P’eclet 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 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 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.

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