Is there a universal log law for turbulent wall-bounded flows?

The history and theory supporting the idea of a universal log law for turbulent wall-bounded flows are briefly reviewed. The original idea of justifying a log law from a constant Reynolds stress layer argument is found to be deficient. By contrast, it is argued that the logarithmic friction law and velocity profiles derived from matching inner and outer profiles for a pipe or channel flow are well-founded and consistent with the data. But for a boundary layer developing along a flat plate it is not, and in fact it is a power law theory that seems logically consistent. Even so, there is evidence for at least an empirical logarithmic fit to the boundary-friction data, which is indistinguishable from the power law solution. The value of κ≈0.38 obtained from a logarithmic curve fit to the boundary-layer velocity data, however, does not appear to be the same as for pipe flow for which 0.43 appears to be the best estimate. Thus, the idea of a universal log law for wall-bounded flows is not supported by either the theory or the data.

[1]  J. Lumley,et al.  A First Course in Turbulence , 1972 .

[2]  Donald W. Smith,et al.  Skin-Friction Measurements in Incompressible Flow , 1958 .

[3]  T. Kármán,et al.  Mechanische Ahnlichkeit und Turbulenz , 1930 .

[4]  Alexander Smits,et al.  Further observations on the mean velocity distribution in fully developed pipe flow , 2004, Journal of Fluid Mechanics.

[5]  Michel Stanislas,et al.  Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry , 2005, Journal of Fluid Mechanics.

[6]  M. V. Zagarola,et al.  Friction factors for smooth pipe flow , 2004, Journal of Fluid Mechanics.

[7]  Jens M. Österlund,et al.  Experimental studies of zero pressure-gradient turbulent boundary layer flow , 1999 .

[8]  A. Smits,et al.  Mean-flow scaling of turbulent pipe flow , 1998, Journal of Fluid Mechanics.

[9]  Luciano Castillo,et al.  Zero-Pressure-Gradient Turbulent Boundary Layer , 1997 .

[10]  Javier Jiménez,et al.  Self-similar vortex clusters in the turbulent logarithmic region , 2006, Journal of Fluid Mechanics.

[11]  Donald Coles,et al.  THE YOUNG PERSON'S GUIDE TO THE DATA , 1968 .

[12]  D. Coles The law of the wake in the turbulent boundary layer , 1956, Journal of Fluid Mechanics.

[13]  W. George Recent Advancements Toward the Understanding of Turbulent Boundary Layers , 2005 .

[14]  Martin Wosnik,et al.  A theory for turbulent pipe and channel flows , 2000, Journal of Fluid Mechanics.

[15]  W. Tollmien,et al.  Zur turbulenten Strömung in Rohren und längs Platten , 1961 .

[16]  F. Clauser The Turbulent Boundary Layer , 1956 .

[17]  M. Oberlack A unified approach for symmetries in plane parallel turbulent shear flows , 2001, Journal of Fluid Mechanics.

[18]  Arne V. Johansson,et al.  A note on the overlap region in turbulent boundary layers , 2000 .