The paper presents an extension of the diagnostic-plot scaling (Alfredsson et al., 2012) of the turbulence-intensity profiles for the outer region of adverse-pressure-gradient (APG) turbulent boundary layers (TBLs). An extended formula including the shape factor is proposed, which allows the diagnostic-plot scaling to be used in strong APGs at high Reynolds numbers. The validity of the new formulation is verified using several available databases. We demonstrate that the new formula allows to scale profiles in cases where the Clauser–Rotta pressure-gradient parameter $\beta$ is below 14 even in presence of very strong flow-history effects. In order to extend the scaling to the near-wall region of TBLs the adapted complete difference function is proposed. The proposed scaling yields a unified description of the turbulence-intensity profiles regardless of their flow history (as opposed to other previously proposed scalings), and is valid for a wider range of cases not only for the outer but also for the inner region.

本文提出了逆压梯度（APG）湍流边界层（TBLs）外部区域湍流强度剖面的诊断图尺度的扩展（Alfredsson等人，2012）。提出了包括形状因子的扩展公式，该公式允许在高雷诺数的强APG中使用诊断图缩放比例。使用几个可用的数据库验证了新配方的有效性。我们证明了新的公式可以在Clauser-Rotta压力梯度参数的情况下缩放轮廓$\beta$即使存在非常强的流动历史效应，该值仍低于14。为了将缩放扩展到TBL的近壁区域，提出了自适应的完全差分函数。所提出的缩放比例对湍流强度分布进行了统一的描述，而与流动历史无关（与其他先前提出的缩放比例相对），并且不仅对于外部区域而且对于内部区域都适用于更广泛的情况。