Coles, Donald (1957) Remarks on the Equilibrium Turbulent Boundary Layer. Journal of the Aeronautical Sciences , 24 (7). pp. 495506. ISSN 19369956. http://resolver.caltech.edu/CaltechAUTHORS:20130510085903873

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Abstract
Two similarity laws are known for the meanvelocity profile in a turbulent boundary layer with constant pressure. These are Prandtl's law of the wall and Karman's momentumdefect law. The first law has recently been generalized empirically to flows with arbitrary pressure gradient by Ludwieg and Tillmann, and the second law to a certain class of equilibrium flows by F. Clauser. In the present paper it is shown that the pressure distribution corresponding to a given equilibrium flow cam be computed by assuming that a certain parameter D = (τ_w/q)dq/dτ_w is constant, where q and τ_w are the dynamic pressure in the free stream and the shearing stress at the wall, respectively. The hypothesis D = constant is suggested by a study of the integrated continuity equation and is supported by a rigorous analogy between the class of equilibrium flows defined by Clauser and the class of laminar flows studied by Falkner and Skan. The hypothesis D = constant is also verified using experimental data for several equilibrium turbulent flows and is interpreted physically from a kinematic point of view. Two hypothetical limiting cases of equilibrium flow are described. At one extreme is the boundary Layer in a sink flow, with a completely logarithmic meanvelocity profile outside the sublayer. At the other extreme is a continuously separating boundary layer in a dimensionless pressure gradient (x/q)dq/dx approximately twice that for the corresponding laminar flow. Typical shearingstress profiles are computed for several equilibrium turbulent flows, including the two limiting cases.
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Additional Information:  © 1957 Institute of the Aeronautical Sciences. Received June 28, 1956. Revised and received February 14, 1957. 
Record Number:  CaltechAUTHORS:20130510085903873 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20130510085903873 
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ID Code:  38413 
Collection:  CaltechAUTHORS 
Deposited By:  Tony Diaz 
Deposited On:  10 May 2013 22:34 
Last Modified:  17 Oct 2014 22:57 
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