二维均匀剪切湍流的湍涡闭合方案

Turbulent-Eddy Closure Scheme for Two-Dimensional Homogeneous Turbulent Shear Flow

通过仔细分析Thorpe与Woods等对湍流的典型实验,得到如下结论:(1)提出了湍流的太极模型;(2)指出了湍流串级的内容包括2个内容,一是湍流外圈层(大涡)在内旋到内部时产生新的圈层(小涡),二是在阴阳旋臂相切的锋面由于依然存在较大切变而产生新的次尺度湍涡;(3)指出湍流的耗散机制是通过湍涡,把具有切变的2流场的交界面通过旋转而无限拉长以增大2者的接触面积,加强了交界面之间的分子交换,从而实现了湍流层层混合的高效率;(4)基于湍涡结构,提出了湍涡闭合方案,给出了Reynolds应力的表达式,闭合了雷诺方程;(5)混合长反映了湍涡的大小,Karman常数则反映了湍涡内外半径比的关系;(6)指出Reynolds方程算子是湍流方程推导的关键,提出了湍流算子的概念;(7)推导出了新型的湍流运动方程;(8)提出了关系不变性原理。

After anatomizing the typical experiments for turbulence by Thorpe and Woods et al. , some results are obtained as follows： （ 1 ） a Taichi model for turbulence is brought forward ; （2） The cascade of turbulence includes two basic contents ： one is the small - scale eddies resulted from the large - scale eddies by their inward - rotation motions, the other is the hypo - scale eddies originated from the front which is a bigger-speed -shear interface separating the fluids from each other; （3） The dissipative mechanism of turbulence is associated with the front which always tends to be drawn very long. As a result, the interface linking two fluids is extended infinitely and the process of the molecular diffusion between the interface is then highly enhanced to achieve the high effective diffusion of turbulence; （4） An eddy closure scheme is brought forward to close the Reynolds equations ; （5） The mixing length is equal to the outer radius of a turbulent eddy, while Karman constant is a function of ratio of inner radius to outer radius of the eddy; （6） By the ideas of operator and turbulent operator, the actual turbulent dynamical equations are deduced; （7） The invariance principle of relationship is brought forward. What＇ s more, counter - gradient transport and eddy relationology are also discussed.