Reynolds stress
= Reynolds stress
{c}
{title2=$R_{ij}=\rho\overline{u_i'u_j'}$}
{wiki}
Velocity-fluctuation covariances transport mean momentum. For positive wall shear, $-\overline{u'w'}$ is the downward momentum-transport magnitude and contributes to the total shear stress. Some stress conventions include the minus sign in the definition of the tensor itself; the momentum equation must use the same convention.