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

*(English)*Zbl 1152.76412Summary: 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 |

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\textit{H. M. Nagib} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 365, No. 1852, 755--770 (2007; Zbl 1152.76412)

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##### References:

[1] | J AEROSP SCI 2 pp 91– (1954) |

[2] | Crighton, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 335 (1602) pp 313– (1973) · Zbl 0314.76062 · doi:10.1098/rspa.1973.0128 |

[3] | J FLUID MECHANICS 422 pp 319– (2000) |

[4] | PROG AEROSP SCI 32 pp 245– (1996) |

[5] | APPL MECH REV 50 pp 689– (1997) |

[6] | PHYS FLUIDS 18 pp 1– (2006) |

[7] | PHYS FLUIDS 16 pp 4586– (2004) |

[8] | EXP FLUIDS 35 pp 389– (2003) |

[9] | J FLUID MECHANICS 187 pp 61– (1988) |

[10] | J FLUID MECHANICS 373 pp 33– (1998) |

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