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Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. (English) Zbl 1152.76412
Summary: 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 $$C_{\text f}$$ behaviour when modified and underpinned by the same experimental data. The variation of the integral parameter, $$H$$, shows consistent agreement between the experimental data and the relation from classical theory. In accordance with the classical theory, the ratio of $$\Delta$$ and $$\delta$$ 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, $$\Pi$$, 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.

##### MSC:
 76F40 Turbulent boundary layers
##### Keywords:
asymptotic; high Reynolds number; boundary layers; scaling
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