Low Reynolds number effect in wall-bounded turbulence*

The deviation of the mean flow from the canonical law of the wall at low Reynolds numbers is often attributed to the low Reynolds number effect. 

The presence of the low Reynolds number effect in the mean flow poses a challenge to near-wall turbulence modeling and necessitates high Reynolds numbers in many contexts.

Furthermore, it suggests distinct flow physics at low and high Reynolds numbers.

This work introduces a velocity scaling that, based on assumptions relevant to the logarithmic layer only, aligns velocity profiles at both low and high Reynolds numbers with the law of the wall.

The contribution is threefold.

Firstly, our derivation identifies the cause of the low Reynolds number effect, i.e., a non-constant total shear stress.

Secondly, the existence of the present scaling suggests a consistent underlying physics governing the mean flow across all Reynolds numbers---this could fundamentally change the present understanding of wall-bounded turbulent flows.

Lastly, through the present scaling, we achieve a more accurate near-wall closure.