标题： 瑞利数和普朗特数在瑞利-贝纳德湍流主体中的标度关系 显示英文标题

标题： Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Benard turbulence

摘要： 雷利（Ra）数和普朗特（Pr）数对努塞尔（Nu）数、雷诺（Re）数、温度波动以及动能和热耗散率的标度进行了研究，针对（数值）均匀雷利亚-贝纳德湍流，即在所有方向上具有周期性边界条件并且通过平均梯度对温度场进行体积强迫的雷利亚-贝纳德湍流。 该系统作为雷利亚-贝纳德流动主体的模型系统，因此作为所谓的“热对流终极状态”的模型。 就Nu和Re的Ra依赖性而言，我们确认了先前的结果\cite{loh03}，这些结果与Kraichnan理论\cite{kra62}和Grossmann-Lohse（GL）理论\cite{gro00,gro01,gro02,gro04}一致，两者均预测$Nu \sim Ra^{1/2}$和$Re \sim Ra^{1/2}$。 然而在这两种理论中Pr的依赖性不同。 在这里，我们表明数值数据与GL理论$Nu \sim Pr^{1/2}$，$Re \sim Pr^{-1/2}$一致。 对于热耗散率和动能耗散率，我们发现$\eps_\theta/(\kappa \Delta^{2}L^{-2}) \sim (Re Pr)^{0.87}$和$\eps_u/(\nu^3 L^{-4}) \sim Re^{2.77}$，也均与GL理论一致，而温度波动不依赖于Ra和Pr。 最后，研究了热量传输的动力学，并置于Doering等人最近的理论发现\cite{doe05}的背景下。 显示英文摘要

摘要： The Rayleigh (Ra) and Prandtl (Pr) number scaling of the Nusselt number Nu, the Reynolds number Re, the temperature fluctuations, and the kinetic and thermal dissipation rates is studied for (numerical) homogeneous Rayleigh-Benard turbulence, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient. This system serves as model system for the bulk of Rayleigh-Benard flow and therefore as model for the so called ``ultimate regime of thermal convection''. With respect to the Ra dependence of Nu and Re we confirm our earlier results \cite{loh03} which are consistent with the Kraichnan theory \cite{kra62} and the Grossmann-Lohse (GL) theory \cite{gro00,gro01,gro02,gro04}, which both predict $Nu \sim Ra^{1/2}$ and $Re \sim Ra^{1/2}$. However the Pr dependence within these two theories is different. Here we show that the numerical data are consistent with the GL theory $Nu \sim Pr^{1/2}$, $Re \sim Pr^{-1/2}$. For the thermal and kinetic dissipation rates we find $\eps_\theta/(\kappa \Delta^{2}L^{-2}) \sim (Re Pr)^{0.87}$ and $\eps_u/(\nu^3 L^{-4}) \sim Re^{2.77}$, also both consistent with the GL theory, whereas the temperature fluctuations do not depend on Ra and Pr. Finally, the dynamics of the heat transport is studied and put into the context of a recent theoretical finding by Doering et al. \cite{doe05}.