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.