常数速度梯度时均匀湍流的二元速度关联函数

在湍流脉动速度比较小的条件下,本文得到了富氏变换过后脉动速度方程的解.它所代表的涡旋,在平均速度梯度为小量时,化为具有常数平均速度梯度的、组成后期均匀各向同性湍流场的涡旋和组成后期各向异性湍流场的涡旋.利用不同时刻的这种涡旋解,组成定常的有常数平均速度梯度的湍流场,这个湍流场可以近似地表达槽流和管流近中心区域的湍流场.我们求得了这种湍流场的二元速度关联函数,包括纵向的关联系数f(γ/λ)和横向的关联系数g(γ/λ).并且和均匀各向同性湍流实验中的前期和后期的f(γ/λ)和g(γ/λ)进行了比较.并且弄清楚了速度梯度对关联系数f(γ/λ)所产生的影响,最后还得到了雷诺应力和涡旋粘性系数的表达式.

The Double Velocity Correlation Function of Homogeneous Turbulence with Constant Mean Velocity Gradient

In this article, as the velocity gradient is taken as a constant value, we obtain the solutions of the equation of fluctuation velocity after Fourier transformation.Under the condition of the the mean velocity gradient being small, they represent the picture of eddies, of whick the homogeneous turbulence(both isotropic and non-isotropic)of the final period is composed. By using the eddies of these types at different times, we may compose the steady turbulent field with the constant velocity gradient and this field may represent the turbulent field in the central part of the channel flow or pipe flow approximately.Then we may obtain the double velocity correlation function of this turbulent field, which involves both longitudinal correlation coeffict f(γ/λ) and the transversal correlation coefficientg(γ/λ).We compare theoretical coefficients with the experimental data of these coefficients at initial period and final period of isotropic homogeneous turbulence. And then we obtain the relation-ship bettyeen the turbulent double velocity correlation coefficient f(γ/λ) and the mean velocity gradient. Finally,we get the expressions of the keynolds stress and the eddy viscosity coefficient.