Abstract: About forty years ago Prof. Zhou and Tsai had suggested a statistical theory of the axisymmetric vortices structure of homogenous isotropic turbulence. Now it was generalized to nonaxisymmetric vortices case. A Zhou-Saffman average method is used to study the statistical average rules. An exact general calculating formula of the orientation average is given. It can decrease the calculating time of the high order correlation functions and moments greatly.

Key words: nonaxisymmetric vortices, orientation average, high order moments

摘要： 将周培源教授于50年代提出的轴对称旋涡结构的湍流统计理论进一步推广到非轴对称旋涡结构的情况，并用周培源-萨夫曼平均方法和张量分析给出了计算方向平均的一般公式，从而大大减少了各种关联函数计算的工作量。

关键词: 非轴对称旋涡, 方向平均, 高阶矩