L'vov Victor S, Pomyalov Anna, Procaccia Itamar, Zilitinkevich Sergej S
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jan;73(1 Pt 2):016303. doi: 10.1103/PhysRevE.73.016303. Epub 2006 Jan 19.
We construct a simple analytic model for wall-bounded turbulence, containing only four adjustable parameters. Two of these parameters are responsible for the viscous dissipation of the components of the Reynolds stress tensor. The other two parameters control the nonlinear relaxation of these objects. The model offers an analytic description of the profiles of the mean velocity and the correlation functions of velocity fluctuations in the entire boundary region, from the viscous sublayer, through the buffer layer, and further into the log-law turbulent region. In particular, the model predicts a very simple distribution of the turbulent kinetic energy in the log-law region between the velocity components: the streamwise component contains a half of the total energy whereas the wall-normal and cross-stream components contain a quarter each. In addition, the model predicts a very simple relation between the von Kármán slope k and the turbulent velocity in the log-law region v+ (in wall units): v+=6k. These predictions are in excellent agreement with direct numerical simulation data and with recent laboratory experiments.
我们构建了一个用于壁面约束湍流的简单解析模型，该模型仅包含四个可调参数。其中两个参数负责雷诺应力张量各分量的粘性耗散。另外两个参数控制这些量的非线性弛豫。该模型对整个边界区域内的平均速度分布以及速度涨落相关函数提供了解析描述，范围从粘性底层，经过缓冲层，再到对数律湍流区域。特别地，该模型预测了对数律区域内湍动能在速度分量之间的一种非常简单的分布：流向分量包含总能量的一半，而壁法向分量和横向分量各包含四分之一。此外，该模型预测了冯·卡门斜率k与对数律区域内的湍流速度v +（以壁面单位计）之间的一种非常简单的关系：v += 6k。这些预测与直接数值模拟数据以及最近的实验室实验结果高度吻合。
