Lagrange与Euler时间积分尺度之间关系的统计动力学物理模型

本文给出了平稳、均匀湍流中平衡涡度及非平衡涡度偏差的定义,建立了Euler及Lagra-nge湍流的随机动力微分方程,解出了各自相关函数。在各向同性及冻结湍流假设中使用Bla-ton公式按上述相关函数解出了Langrange时间尺度与Euler尺度比的表达式,其渐近值恰为全方向湍流度的倒数的1/2~(1/2)倍即0.71/i。

THE RANDOM DYNAMIC THEORY ON THE RELATION BETWEEN LAGRANGIAN AND EULERIAN TIME SCALE

In this paper the "Bernoulli's Equilibrium Vorticity" and the "Deviation of the BEV" are defined and a random dynamic model, which can give both Lagrangian and Eulerian autocorrelation functions, are set up for wind velocity fluctuations in the stationary, homogeneous turbulence. Under Taylor}s hypothesis of "frizened eddies", the ratio of Lagrangian time scale to Eulerian is given as a function of the deviation of wind diraction, that has asymptotic form 0.71/i where i is the intensity of the turbulence, if the turbulence is isotropic.