State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, China.
Phys Rev Lett. 2012 Aug 3;109(5):054502. doi: 10.1103/PhysRevLett.109.054502. Epub 2012 Jul 31.
A series of Mach-number- (M) invariant scalings is derived for compressible turbulent boundary layers (CTBLs), leading to a viscosity weighted transformation for the mean-velocity profile that is superior to van Driest transformation. The theory is validated by direct numerical simulation of spatially developing CTBLs with M up to 6. A boundary layer edge is introduced to compare different M flows and is shown to better present the M-invariant multilayer structure of CTBLs. The new scalings derived from the kinetic energy balance substantiate Morkovin's hypothesis and promise accurate prediction of the mean profiles of CTBLs.
提出了一系列可压缩湍流边界层（CTBL）的马赫数不变量标度，得到了一种优于范德雷斯变换的粘性加权平均速度分布变换。该理论通过高达 6 的马赫数的空间发展 CTBL 的直接数值模拟进行了验证。引入边界层边缘来比较不同的马赫数流动，并展示了更好地呈现 CTBL 的马赫数不变多层结构。从动能平衡中推导出的新标度证实了莫罗文假设，并有望准确预测 CTBL 的平均轮廓。
