关键词: 湍流;侧偏平均;正交各向异性;理性控制方程

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