dorsal/arxiv
View SchemaThe persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows
| Authors | Katepalli R. Sreenivasan, Anupam Sahay |
|---|---|
| Categories | |
| ArXiv ID | physics/9708016 |
| URL | https://arxiv.org/abs/physics/9708016 |
Abstract
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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"abstract": "We argue that important elements of the dynamics of wall-bounded flows reside\nat the wall-normal position $y_p^+$ corresponding to the peak of the Reynolds\nshear stress. Specializing to pipe and channel flows, we show that the mean\nmomentum balance in the neighborhood of $y_p^+$ is distinct in character from\nthose in the classical inner and outer layers. We revisit empirical data to\nconfirm that $y_p^+ = O(R^{1/2})$ and show that, in a neighborhood of order\n$R^{1/2}$ around $y_p^+$, only the viscous effects balance pressure-gradient\nterms. Here, R is the Reynolds number based on friction velocity and pipe\nradius (or channel half-width). This observation provides a mechanism by which\nviscous effects play an important role in regions traditionally thought to be\ninviscid or inertial; in particular, it throws doubt on the validity of the\nclassical matching principle. Even so, it is shown that the classical\nsemi-logarithmic behavior for the mean velocity distribution can be a useful\napproximation. It is argued that the recently advanced power-law profiles\npossess a rich underlying structure, and could be good approximations to the\ndata over an extended region (but they too are unlikely to be exact).",
"arxiv_id": "physics/9708016",
"authors": [
"Katepalli R. Sreenivasan",
"Anupam Sahay"
],
"categories": [
"physics.flu-dyn",
"chao-dyn",
"cond-mat.stat-mech",
"nlin.CD"
],
"title": "The persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows",
"url": "https://arxiv.org/abs/physics/9708016"
},
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