Abstract: This paper gives a review on the study of the Gao-Yong rational theory of turbulence during the last decade.The detailed derivation of the Gao-Yong equations of compressible turbulent flow is presented.Based on the unilateral statistical average scheme to capture the first-order statistical information of the fluctuation field,the theory built up continuity and momentum equations of the fluctuation field.It also allows one to formulate theories of orthotropic turbulence and momentum transfer chain in the modeling of correlation terms,and eventually leads to a complete closed set of equations of turbulent flow without empirical coefficients and wall functions.The independent mechanical energy equation of drift flow,derived in a series form to reflect typical multi-scale nonlinear phenomena of turbulence,plays a key role for describing statistical mean behaviors and various-order coherent structures of turbulent flow.A wide range of flow cases,including many well-known difficult problems of turbulence,have been solved by the newly derived equations.The adaptability of the equations to various turbulent flows and their strong ability for engineering application have been preliminarily verified.

Key words: Turbulent flow;Unilateral average;Orthothropic turbulence;Rational control quation

摘要： 对近十年来Gao-Yong理性湍流方程的研究进行综述,给出矢量形式的可压湍流封闭方程组的推导过程。侧偏统计平均保留了湍流脉动量的一阶统计信息,在引入加权漂移速度对称性及正交各向异性后,导出了漂移流的连续方程、动量方程及机械能方程,最后依据湍流物理的唯象论,使用动量传输链概念模化封闭了整个方程组。方程组不含任何经验系数,不使用壁面函数,保留了NS方程的均化的非线性特性。其级数形式的能量方程与非线性现象多尺度层次现象相对应,具备了描述湍流统计平均流动及拟序结构流动的双重功能。已进行了大量算例验证,验证结果证明了Gao-Yong湍流方程对广泛范围的复杂湍流问题的适定性。

关键词: 湍流;侧偏平均;正交各向异性;理性控制方程