湍流通用物理方程的推导及讨论

湍流的通用方程已经获得。利用变形率张量与摄动变形位移的点积分解湍流脉动速度,并使用密度加权的侧偏系综平均方法取代Reynolds平均方法,对Navier-Stokes方程进行平均。在二阶精度上没有出现未知相关量,从而获得了具有二阶精度的封闭的湍流通用物理方程。方程中无相关量,不引入任何经验系数,无需构造任何湍流模型,即可描述任意复杂湍流场并解释湍流物理本质。方程在长时标上描述湍流平均行为,在短时标上描述相应尺度层次的湍流结构现象,从而统一了湍流的统计及结构二大学派。方程简化后得到湍流的规范方程,是混合的Burgers-Korteweg-de Vries方程,对该方程的分析给出了湍流转捩准则。文中对湍流的间歇性、拟序结构、各向异性、湍流能量逆转等现象的物理本质进行了初步讨论。 

DERIVATION OF THE UNIVERSAL PHYSICAL EQUATION OF TURBULENCE AND ITS CANONICAL FORM

The fully- detailed derivation of the universal physical equation ofturbulence has been given. Instead of the conventional Reynolds average, a new method, named off-center ensemble average, is used to obtain the equation. Through some mathematical approximations and without introducing any empirical coefficients, the equation may provide a secondary order of accuracy, which satisfies the needs of engineering study of turbulence. In one-dimensional case, the momentum equation of turbulence is simplified as the mixed Burgers-Korteveg de Vries equation-the canonical equation of turbulence. The analysis of the Burgers-Kerteweg-de Vries equation gives the criterion of transition. The physical meaning of the equations is briefly discussed. It shows that dissipation and dispersion coexist as two basic physical principles of turbulence. The development of dissipation is monotonic, describing the conversion of the kinetic turbulence energy into heat due to viscosity. Dispersion can be either positive or negative. It represents the energy transformation between the mean flow and the large and micro-eddies before the energy is finally dissipated into molecular heat. Positive dispersion corresponds to cascading down process and negative dispersion means collection of energy. The mechanison of intermittency and anisotropy, and the effects of noise and developing history on turbulence are also discussed.