In this study, we exploit the Renard-Deck identity [J. Fluid Mech. 790, 339 (2016)] to decompose the mean friction drag in adverse-pressure-gradient turbulent boundary layers (APG-TBLs) into three components, associated with viscous dissipation, turbulence kinetic energy production, and spatial growth of the flow, respectively. We consider adverse-pressure-gradient turbulent boundary layers developing on flat plates and airfoils, with friction Reynolds numbers in the range $200<{\text{Re}}_{\tau }<2000$, and with Rotta-Clauser pressure-gradient parameters ($\beta$) ranging from 0 to 50. The effects of Reynolds number, adverse pressure gradient, and the pressure-gradient history on the contributing components are individually investigated, and special attention is paid to the comparisons with zero-pressure-gradient turbulent boundary layers (ZPG-TBLs). Our results indicate that the inner peaks of the dissipation and production terms are located at $y^{+}\approx 6$ and $y^{+}\approx 16.5$, respectively, and their outer peaks scale with the $99\%$ boundary-layer thickness (${\delta }_{99}$), i.e., $y/{\delta }_{99}\approx 0.7$ and $0.53$, respectively. These results are independent of the friction Reynolds number, the magnitude of $\beta$, and its development history. Moreover, the spatial-growth component is negative in the investigated APG-TBLs, and its magnitude increases with $\beta$.

中文翻译：

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反压力梯度湍流边界层中平均摩擦阻力的分解

在这项研究中，我们利用Renard-Deck身份[ J. Fluid Mech。 [790，339（2016）]将逆压梯度湍流边界层（APG-TBLs）中的平均摩擦阻力分解为三个部分，分别与粘性耗散，湍流动能产生和流的空间增长相关。我们考虑在平板和机翼上形成逆压力梯度湍流边界层，其摩擦雷诺数在$200<{\text{回覆}}_{\tau }<2000$，并带有Rotta-Clauser压力梯度参数（$\beta$），范围从0到50。分别研究了雷诺数，不利的压力梯度和压力梯度历史对作用分量的影响，并特别注意与零压力梯度湍流边界层（ZPG）的比较-TBL）。我们的结果表明，耗散和生产项的内峰位于${ÿ}^{+}\approx 6$ 和 ${ÿ}^{+}\approx 16.5$，它们的外峰随 $99％$ 边界层厚度（${\delta }_{99}$），即 $ÿ/{\delta }_{99}\approx 0.7$ 和 $0.53$， 分别。这些结果与摩擦雷诺数，$\beta$，及其发展历史。此外，在研究的APG-TBL中，空间增长分量为负，并且其大小随$\beta$。