×

Is there a universal log law for turbulent wall-bounded flows? (English) Zbl 1152.76405

Summary: 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 \(\kappa \approx 0.38\) 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.

MSC:

76F40 Turbulent boundary layers
Full Text: DOI

References:

[1] J FLUID MECHANICS 535 pp 143– (2004)
[2] ADV APPL MECH IV pp 1– (1954)
[3] J FLUID MECHANICS 1 pp 191– (1956)
[4] PROC AFOSRIFPSTANFORD CONF ON COMPUATION OF TURBULENT BOUNDARY LAYERS vol. 2 pp 1– (1968)
[5] J FLUID MECHANICS 561 pp 329– (2006)
[6] AIAA J 44 pp 2435– (2006)
[7] APPL MECH REV 50 pp 689– (1997)
[8] TECH PHYS USSR IV pp 155– (1937)
[9] J FLUID MECHANICS 501 pp 135– (2004)
[10] J FLUID MECHANICS 511 pp 41– (2004)
[11] J FLUID MECHANICS 427 pp 229– (2001)
[12] PHYS FLUIDS 12 pp 1– (2000)
[13] NACHR GES WISS MATHPHYS KLASSE GTTINGEN 5 pp 58– (1930)
[14] J FLUID MECHANICS 421 pp 115– (2000)
[15] J FLUID MECHANICS 373 pp 33– (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.