标题： 普朗特数对可压缩对流的影响：流动统计量和对流能量传输 显示英文标题

标题： Prandtl number dependence of compressible convection: Flow statistics and convective energy transport

摘要： （摘要）背景：恒星对流层中运动粘度与热扩散率的比值，即普朗特数，远小于1。目标：研究对流流动和能量传输随普朗特数的变化统计特性。方法：使用三维数值模拟研究笛卡尔几何中的对流。对流区（CZ）位于两个稳定分层层之间。分别研究上升流和下降流的统计特性和传输特性。结果：均方根速度随着普朗特数的减小而增加。同时，下降流的填充因子减小，导致在较低普朗特数下出现更强的下降流，并且越池现象对普朗特数有很强的依赖性。速度功率谱随普朗特数的变化不明显。在最高雷诺数下，速度功率谱与博利亚诺-奥布霍夫$k^{-11/5}$标度相容。水平平均的对流能量通量（$\overline{F}_{\rm conv}$）在对流区内与普朗特数无关。然而，在低（高）普朗特数下，上升流（下降流）是主要的对流通量贡献。这些结果与低普朗特数区域中的瑞利-贝纳德对流相似，在该区域对流剧烈湍流但能量传输效率低。结论：当前结果表明对流越池和能量通量对普朗特数有很强的依赖性。天体物理对流的数值模拟通常使用普朗特数为1。当前结果表明这可能导致误导性的结果，并且天体物理相关的低普朗特数区域在定性上不同于典型模拟所探索的参数区域。 显示英文摘要

摘要： (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 Prandtl number. Methods: Three-dimensional numerical simulations convection in Cartesian geometry are used. The convection zone (CZ) is embedded between two stably stratified layers. Statistics and transport properties of up- and downflows are studied separately. Results: The rms velocity increases with decreasing Prandtl number. At the same time the filling factor of downflows decreases and leads to stronger downflows at lower Prandtl numbers, and to a strong dependence of overshooting on the Prandtl number. Velocity power spectra do not show marked changes as a function of Prandtl number. At the highest Reynolds numbers the velocity power spectra are compatible with the Bolgiano-Obukhov $k^{-11/5}$ scaling. The horizontally averaged convected energy flux ($\overline{F}_{\rm conv}$) is independent of the Prandtl number within the CZ. However, the upflows (downflows) are the dominant contribution to the convected flux at low (high) Prandtl number. These results are similar to those from Rayleigh-Ben\'ard convection in the low Prandtl number regime where convection is vigorously turbulent but inefficient at transporting energy. Conclusions: The current results indicate a strong dependence of convective overshooting and energy flux on the Prandtl number. Numerical simulations of astrophysical convection often use Prandtl number of unity. The current results suggest that this can lead to misleading results and that the astrophysically relevant low Prandtl number regime is qualitatively different from the parameters regimes explored in typical simulations.