(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！