Persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows

We expand on our previous argument (Sreenivasan 1987) that important elements of the dynamics of wall-bounded flows reside at the wall-normal position y_p corresponding to the peak of the Reynolds shear stress. Specializing to pipe and channel flows, we show that the mean momentum balance in the neighborhood of y_p is distinct in character from those in the classical inner and outer layers. We revisit empirical data to confirm that the y_p = O((hν/U_*) ^1/2 ) and show that, in a neighborhood of order R_* ^1/2 around y_p, only the viscous effects balance pressure-gradient terms. Here, R_* = hU_*/ν, h is the pipe radius or channel half-width, ν is the kinematic viscosity of the fluid and U_* is the friction velocity. This observation provides a mechanism by which viscous effects play an important role in regions traditionally thought to be inviscid; in particular, it throws doubt on the validity of the classical matching principle. Even so, it is shown that the classical semi-logarithmic behavior for the mean velocity distribution can be a valid approximation. It is argued that the recently advanced power-law profiles possess a rich underlying structure, and could be good approximations to the data over an extended region (but they too are unlikely to be exact).