湍流Rayleigh-Bénard热对流温度剖面中对数律研究

Logarithmic mean temperature profiles in turbulent Rayleigh-Bénard convection

本文采用湍流热对流的并行直接数值模拟(Parallel Direct Method of Direct Numerical Simulation,PDM-DNS),计算了系列Ra数的二维方腔Rayleigh-Bénard热对流.选取典型Ra=10^(10),Pr=4.3,讨论了流动平均场的近底板区域温度分布.温度边界层沿横向可分为三个区域:羽流发射区、冲击区和大尺度环流剪切区.在羽流发射区温度剖面存在对数律,冲击区和大尺度环流剪切区没有明显的对数律特征.横向平均得到的温度剖面也存在对数律.研究系列Ra数的横向平均温度剖面,得到温度变化满足A×log(y)+B的关系,温度剖面对数律振幅–A和Ra数呈现标度关系–A^Ra^(–0.145),与实验中发现的关系基本一致.

Results of two-dimensional turbulent Rayleigh-Bénard （RB） convection based on the parallel direct method of direct numerical simulation （PDM-DNS） in sample of aspect ratio Г=1 up to Rayleigh number Ra=10^12 are presented. Mean temperature field near the bottom of the sample for Ra=10^10 and Pr=4.3 is studied. The boundary layer of Rayleigh-Bénard convection can be divided horizontally into three regions, namely, ejecting region where thermal plumes are emitted, impacting region and large-scale circulation shearing region. The temperature profile is logarithmic in the ejecting region while the logarithmic behavior is not visible in the impacting region and the large-scale circulation sheafing region. In addition, the horizontally averaged profile also reveals a logarithm. The horizontally averaged temperature varies as A×log（y）＋B with the distance y from the bottom plate of the sample. The log amplitude -A scales as Ra-0.145, in good agreement with the experiment.