论文标题
在动荡的热对流中重新访问雷诺和努塞尔数
Revisiting Reynolds and Nusselt numbers in turbulent thermal convection
论文作者
论文摘要
在本文中，我们扩展了Grossmann和Lohse（GL）模型[Phys。莱特牧师。 {\ bf 86}，3316（2001）]在湍流Rayleigh-Bénard对流（RBC）中的雷诺数（RE）和Nusselt编号（NU）的预测。为了实现这一目标，我们为散装率和边界层的耗散率的预成分使用功能形式。与游离湍流相比，在存在壁和浮力的情况下抑制非线性相互作用以及粘性边界层剖面与Prandtl-Blasius理论的偏差，因此出现了功能形式。我们在一个三维单元框上进行60次数字运行，用于一系列雷利号（RA）和PrandTL数字（PR），并使用机器学习确定上述功能表单。与GL模型的数值和实验结果相比，修订后的预测与过去的数值和实验结果更好，尤其是对于极端的PrandTL数字。
In this paper, we extend Grossmann and Lohse's (GL) model [Phys. Rev. Lett. {\bf 86}, 3316 (2001)] for the predictions of Reynolds number (Re) and Nusselt number (Nu) in turbulent Rayleigh-Bénard convection (RBC). Towards this objective, we use functional forms for the prefactors of the dissipation rates in the bulk and the boundary layers. The functional forms arise due to inhibition of nonlinear interactions in the presence of walls and buoyancy compared to free turbulence, along with a deviation of viscous boundary layer profile from Prandtl-Blasius theory. We perform 60 numerical runs on a three-dimensional unit box for a range of Rayleigh numbers (Ra) and Prandtl numbers (Pr) and determine the aforementioned functional forms using machine learning. The revised predictions are in better agreement with the past numerical and experimental results than those of the GL model, especially for extreme Prandtl numbers.
