论文标题
对流的中尺度湍流在非常低的prandtl数字
Convective mesoscale turbulence at very low Prandtl numbers
论文作者
论文摘要
在自然系统中,水平扩展的湍流对流称为中尺度对流,在实验和模拟中都需要调查一个挑战。对于非常低的分子prandtl数字,例如在恒星对流和地球的外核中,尤其如此。本研究报告了在侧面长度$ l $和高度$ l $和高度$ h $中的动荡雷利 - 纳德对流的三维直接数值模拟,其长宽比$γ= l/h $ 25,prandtl数字几乎占4个学分,差不多4个学分,$ 10^{-3} {-3} \ le pr \ le 7 $ $ 10^5^5^5^5^5^5^5^5^5^5^5^5^5^5^5^5^5^5^5^5.高达$ 5.36 \ times 10^{11} $点的网格上的大规模并行计算。该$ PR $范围的低端无法在受控实验室测量中访问。我们报告了流动的基本特性及其趋势的趋势,尤其是在整个对流层中,动量和热量的全球动量和热量(后者分解为对流和扩散的贡献),温度和温度波动的平均垂直谱,以及动能和热量消散率。我们还探讨了对流层中大部分的湍流在光谱,增量力矩和耗散性异常方面类似于经典的同质和各向同性湍流,并找到了紧密的相似性。最后,我们表明,对于$ pr \ Lessim 0.005 $,对中尺度的订单的特征量表似乎饱和到$λ\ gtrsim 3h $的波长。我们简要地讨论了这些结果对湍流对流的亚网格量表参数化的发展的可能影响。
Horizontally extended turbulent convection, termed mesoscale convection in natural systems, remains a challenge to investigate in both experiments and simulations. This is particularly so for very low molecular Prandtl numbers as in stellar convection and in Earth's outer core. The present study reports three-dimensional direct numerical simulations of turbulent Rayleigh-Bénard convection in square boxes of side length $L$ and height $H$ with the aspect ratio $Γ=L/H$ of 25, for Prandtl numbers that span almost 4 orders of magnitude, $10^{-3}\le Pr \le 7$, and Rayleigh numbers $10^5 \le Ra \le 10^7$, obtained by massively parallel computations on grids of up to $5.36\times 10^{11}$ points. The low end of this $Pr$-range cannot be accessed in controlled laboratory measurements. We report the essential properties of the flow and their trends with Rayleigh and Prandtl numbers, in particular the global transport of momentum and heat -- the latter decomposed into convective and diffusive contributions -- across the convection layer, mean vertical profiles of the temperature and temperature fluctuations, and the kinetic energy and thermal dissipation rates. We also explore the degree to which the turbulence in the bulk of the convection layer resembles classical homogeneous and isotropic turbulence in terms of spectra, increment moments, and dissipative anomaly, and find close similarities. Finally, we show that a characteristic scale on the order of the mesoscale seems to saturate to a wavelength of $λ\gtrsim 3H$ for $Pr\lesssim 0.005$. We briefly discuss possible implications of these results for the development of subgrid scale parameterization of turbulent convection.