Elements and Implications of a
New Theory for Turbulent Wall-Flows

J. C. Klewicki

Physical Fluid Dynamics Laboratory

Department of Mechanical Engineering

University of Utah

Salt Lake City, Utah 84112

The
properties of the mean momentum balance in turbulent boundary layer, pipe and
channel flows are explored both experimentally and theoretically.^{1} Available high quality data reveal a
four-layer description that is a considerable departure from the four layer
structure traditionally and nearly universally ascribed to turbulent wall
flows. Each of the four layers is
characterized by a predominance of two of the three terms in the governing
equations, and thus the mean dynamics of these four layers are unambiguously defined.
The inner normalized physical extent of three of the layers exhibit significant
Reynolds number dependence. The scaling properties of these layer thicknesses
are determined. Particular significance is attached to the viscous/Reynolds
stress gradient balance layer since, for example, its thickness defines a new
length scale. Multiscale analysis
(necessarily incomplete) substantiates the four layer structure in developed
turbulent channel flow. In particular, the analysis verifies the existence of a
third layer, with its own characteristic scaling, between the traditional inner
and outer layers. Other information can be surmised as well, such as (1) the
logarithmic-like character of two distinct regions within the flow, (2) a
flattening of the Reynolds stress profile near its maximum, (3) the scaling of
the widths of the four layers, (4) the mean velocity increment across each
layer, (5) the rate of decay of the mean
velocity gradient, and (6) the asymptotic increase rate of the peak value of
the Reynolds stress. All of these results follow from a systematic train of
reasoning, under the minimal primary assumption that the mean velocity
increases monotonically from the wall.
The physical implications of present results are briefly discussed
relative to boundary layer structure and the effects of surface roughness with
Reynolds number

^{1} The primary results of this presentation
may be found in: Wei, T., Fife, P., Klewicki, J. and McMurtry, P. 2003
“Properties of the mean momentum balance in turbulent boundary layer, pipe and
channel flows,” under review, *J. Fluid Mech*.