Summary Turbulent energy equation based on the Reynolds averaging hypothesis was approximated in the near wall layer and an analytical solution was recently proposed to it by considering that i) the shape function is constant in the equilibrium layer and ii) the turbulent energy dissipation is inversely proportional to the square of the wall distance. In this work, we provide a justification for the constant shape function assumption and revise the second argument with an analytical model with a proper theoretical basis. We then establish an alternative formulation to derive a near wall analytical solution of the turbulent energy equation by further considering length scale variations across the equilibrium layer. Results of the analytical solution are compared against the DNS datasets and found to be in excellent agreement. One of the potential advantages of this near wall analytical solution is to obviate the need for solving the turbulent energy equation near the wall in the RANS, hybrid RANS/LES closures thus resulting in quicker and accurate engineering computations.

中文翻译：

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近壁湍流能方程的解析解

总结 基于雷诺平均假设的湍流能量方程在近壁层近似，最近提出了一个解析解，考虑到 i) 平衡层中的形状函数是常数 ii) 湍流能量耗散成反比到墙距离的平方。在这项工作中，我们为恒定形状函数假设提供了理由，并使用具有适当理论基础的分析模型修改了第二个参数。然后，我们通过进一步考虑跨平衡层的长度尺度变化，建立了一个替代公式，以推导出湍流能量方程的近壁解析解。将分析解决方案的结果与 DNS 数据集进行比较，发现非常一致。