Chattopadhyay A K, Bhattacharjee J K
Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, West Bengal, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Jan;63(1 Pt 2):016306. doi: 10.1103/PhysRevE.63.016306. Epub 2000 Dec 21.
In the turbulent boundary layer above a flat plate, the velocity profile is known to have the form v=v(0)[(1/kappa)ln z+const]. The distance from the wall in dimensionless units is z and v(0) is a uniquely defined velocity scale. The number kappa is universal, and measurements over several decades have shown that it is nearly 0.42. We use a randomly stirred model of turbulence to derive the above law and find kappa=sqrt[108/125pi] approximately 0.52.
在平板上方的湍流边界层中，已知速度剖面具有v = v(0)[(1/κ)ln z + const]的形式。以无量纲单位表示的距壁面距离为z，v(0)是唯一确定的速度尺度。κ值是通用的，几十年来的测量表明它接近0.42。我们使用一个随机搅拌的湍流模型来推导上述定律，得出κ = sqrt[108/125π]，约为0.52。
