(principle) Reynolds (shear) stress (tensor)

peiying

基础不好的小白被这几个 stress 搞得有点stress.
Reynolds stress, Reynolds shear stress, and stress tensor.

原来好像知道什么是Reynolds stress, papers 里前面加个principle,中间加shear, 末尾再加tensor,就发现自己概念不清了. 符号各个paper里还不一样, 也得慢慢对照.

还望大牛给点指点. 我继续掰书去了...

peiying

Turbulent stress 就是 Reynolds stress （Cengel, Fluid Mechanics, 第八章第五节， Turbulent flow in pipes）

Stress Tensor 就是为了突出下是九个方向。（Credit to Yeru）

Reynolds shear stress 有时候等同于 Reynolds stress，有时候特指 $\overline{u^{\prime} v^{\prime}}$。

“$\rho \overline{u^{\prime} v^{\prime}}$ is Reynolds shear stress and $\rho \overline{u^{\prime} u^{\prime}}$ and $\rho \overline{v^{\prime} v^{\prime}}$ are Reynolds normal stresses,” （Choon-Sik Jhun, 2018；Reynolds Stresses，An Internet Book on Fluid Dynamics，http://brennen.caltech.edu/fluidbook/basicfluiddynamics/turbulence/reynoldsstresses.pdf
）
$\rho \overline{u^{\prime} v^{\prime}}=\frac{1}{N} \sum_{1}^{N} \rho(u-\bar{u})(v-\bar{v})$
$\rho \overline{u^{\prime} u^{\prime}}=\frac{1}{N} \sum_{1}^{N} \rho(u-\bar{u})^{2}$
$\rho \overline{v^{\prime} v^{\prime}}=\frac{1}{N} \sum_{1}^{N} \rho(v-\bar{v})^{2}$

Principle RSS
$R S S_{p }=\sqrt{\left(\frac{\rho \overline{u^{\prime} u^{\prime}}-\rho \overline{v^{\prime} v^{\prime}}}{2}\right)^{2}-\left(\rho \overline{u^{\prime} v^{\prime}}\right)^{2}}$
我暂时用不着，不去想了... (Choon-Sik Jhun, 2018, Determination of Reynolds Shear Stress Level for Hemolysis)

几乎全是摘得，要是理解有误还望指正，感谢。

gemini

@peiying

李东岳

$\tau$这个雷诺应力，对角线的是normal stress，非对角线的是shear stress。不过你说的更详细，感谢分享！