Approach to an asymptotic state for zero pressure gradient turbulent boundary layers

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 365; no. 1852; pp. 755 - 770
• Main Authors: Nagib, Hassan M, Chauhan, Kapil A, Monkewitz, Peter A
• Format: Journal Article
• Language: English
• Published: London The Royal Society 15-03-2007
• Subjects: Asymptotic; Boundary Layers; Coefficients; Data ranges; Experimental data; High Reynolds Number; Pressure gradients; Reynolds number; Scaling; Turbulence; Turbulent boundary layer; Velocity distribution
• ISSN: 1364-503X; 1471-2962
• DOI: 10.1098/rsta.2006.1948

shows consistent agreement between the experimental data and the relation from classical theory. In accordance with the
classical theory, the ratio of
is shown to reach an asymptotic value at the highest available experimental Reynolds numbers if correct values of logarithmic-law
constants and an appropriate skin-friction estimate are used. The paper closes with a discussion of the Reynolds number trends
of the outer velocity defect which are important to establish a consistent similarity theory and appropriate scaling.
behaviour when modified and underpinned by the same experimental data. The variation of the integral parameter,
asymptotes to a constant. Then, the usefulness of the ratio of appropriately defined mean and turbulent time-scales to define
and diagnose equilibrium flow is established. Next, the description of mean velocity profiles is revisited, and the validity
of the logarithmic law is re-established using both the mean velocity profile and its diagnostic function. The wake parameter,
Flat plate turbulent boundary layers under zero pressure gradient at high Reynolds numbers are studied to reveal appropriate
scale relations and asymptotic behaviour. Careful examination of the skin-friction coefficient results confirms the necessity
for direct and independent measurement of wall shear stress. We find that many of the previously proposed empirical relations
accurately describe the local
and