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

Details The persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows The persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows

1997-08-13

arxiv.org/abs/physics/9708016v1

Physics

Fluid Dynamics

15 pages, Latex, 7 eps figures, label positions will need adjustment if the text height or width is changed. To appear in `Sel

Scientific paper

We argue 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 $y_p^+ = O(R^{1/2})$ and show that, in a neighborhood of order $R^{1/2}$ around $y_p^+$, only the viscous effects balance pressure-gradient terms. Here, R is the Reynolds number based on friction velocity and pipe radius (or channel half-width). This observation provides a mechanism by which viscous effects play an important role in regions traditionally thought to be inviscid or inertial; 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 useful 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).

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