In the current study, model expressions for fifth-order velocity moments obtained from the truncated Gram-Charlier series expansions model for a turbulent flow field probability density function are validated using data from direct numerical simulation (DNS) of a planar turbulent flow in a strained channel. Simplicity of the model expressions, the lack of unknown coefficients, and their applicability to non-Gaussian turbulent flows make this approach attractive to use for closing turbulent models based on the Reynolds-averaged Navier-Stokes equations. The study confirms validity of the model expressions. It also shows that the imposed flow deformation improves an agreement between the model and DNS profiles for the fifth-order moments in the flow buffer zone including when the flow reverses its direction. The study reveals sensitivity of particularly odd velocity moments to the grid resolution. A new length scale is proposed as a criterion for the grid generation near the wall and in the other flow areas dominated by high mean velocity gradients when higher-order statistics have to be collected from DNS.

在当前的研究中，使用来自平面湍流的直接数值模拟（DNS）数据验证了从湍流场概率密度函数的截断的Gram-Charlier级数展开模型获得的五阶速度矩的模型表达式渠道。模型表达式的简单性，未知系数的缺乏以及它们对非高斯湍流的适用性，使得该方法对于基于雷诺兹平均Navier-Stokes方程的闭合湍流模型具有吸引力。该研究证实了模型表达式的有效性。它还显示，对于流缓冲区域中的五阶矩（包括当流反向时），强加的流变形改善了模型和DNS轮廓之间的一致性。研究表明，特别是奇数速度矩对网格分辨率的敏感性。当必须从DNS收集高阶统计量时，建议使用新的长度尺度作为壁附近和其他以高平均速度梯度为主的流动区域中网格生成的标准。