In-depth analyses of existing direct numerical simulations (DNS) data led to a logical and important classification of generic turbulent boundary layers (TBLs), namely Type-A, -B and -C TBL, based on the distribution patterns of the time-averaged wall-shear stress. Among these types, Type-A TBL and its related law formulations were investigated in terms of the analytical velocity profiles independent on Reynolds number (Re). These formulations were benchmarked by the DNS data of turbulence on a zero-pressure-gradient flat-plate (ZPGFP). With reference to the analysis from von Karman in developing the traditional law-of-the-wall, the current study first physically distinguished the time-averaged local scale used by von Karman from the time-space-averaged scale defined in the current paper, and then derived the governing equations with the Re — independency under the time-space-averaged scales. Based on the indicator function (IDF) and TBL thickness, the sublayer partitions were quantitatively defined. The analytical formulations for entire ZPGFP TBL were derived, including the formula in the inner, buffer, semi-logarithmic (semi-log) and wake layers. The research profoundly understood the damping phenomenon and its controlling mechanism in the TBL with its associated mathematical expressions, namely the damping function under both linear and logarithmic coordinates. Based on these understandings and the quantified TBL partitions, the analytical formulations for the entire ZPGFP TBL were established and were further proved being uniform and consistent under both the time-averaged local and the time-space-averaged scales. Comparing to the traditional law, these formulations were validated by the existing DNS data with more accuracy and wider applicability. The findings advance the current understandings of the conventional TBL theory and its well-known foundation of law-of-the-wall.

中文翻译：

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A型湍流边界层的壁面分析公式

对现有直接数值模拟（DNS）数据的深入分析导致了基于时间分布模式的通用湍流边界层（TBL）的合理且重要的分类，即Type-A，-B和-C TBL。平均墙剪应力。在这些类型中，根据独立于雷诺数（Re）。这些配方通过零压力梯度平板（ZPGFP）上的湍流DNS数据进行基准测试。参照冯·卡曼（von Karman）在开发传统壁垒法方面的分析，本研究首先从物理上将冯·卡曼（von Karman）使用的时间平均局部尺度与本文定义的时空平均尺度区分开来，然后用Re推导控制方程—在时空平均尺度下的独立性。基于指标函数（IDF）和TBL厚度，对子层分区进行了定量定义。得出了整个ZPGFP TBL的分析配方，包括内层，缓冲层，半对数层（半对数层）和尾流层的配方。研究及其相关的数学表达式深刻地理解了TBL中的阻尼现象及其控制机理，即线性和对数坐标下的阻尼函数。基于这些理解和量化的TBL分区，建立了整个ZPGFP TBL的分析公式，并进一步证明了其在时均本地和时空均值范围内是一致且一致的。与传统法律相比 这些公式已通过现有DNS数据进行了验证，具有更高的准确性和更广泛的适用性。这些发现推动了对传统TBL理论及其众所周知的壁垒基础的当前理解。