标题： 关于圆柱体后的分离流：来自最小压强梯度原理的见解 显示英文标题

标题： On the Separating Flow Behind a Cylinder: Insights from the Principle of Minimum Pressure Gradient

摘要： 我们研究了圆柱体上的分离流，有两个目标： (i) 证明曲率匹配条件的有效性， (ii) 在不显式建模边界层的情况下，获得亚临界区域（Re=10^4-10^5）中分离角的合理估计。 首先，我们研究了Roshko的自由流线模型（1954）；这是一个理想流模型，用不连续片表示近尾流区域中的分离剪切层。 该模型无法预测圆柱体上的正确分离角。 Roshko将这种差异归因于曲率匹配条件，该条件断言在分离点处的分离流线的曲率必须与圆柱体的曲率相匹配。 我们证明该条件是合理的，并不是Roshko模型在预测分离时失败的真正原因。 其次，我们采用了最小压力梯度原理（PMPG），该原理断言，不可压缩流通过在域内最小化压力梯度的总大小来演化。 受到在Re=10^4-10^5范围内流动特性相对独立于Re这一事实的鼓舞，我们旨在该区域内预测分离角而不建模边界层——尽管这一任务看似不可能，但Prandtl在其开创性论文（Prandtl 1904）中已有所预期。 在一组运动学允许的平衡流中，我们利用PMPG选出具有最小压力梯度成本的分离流。 有趣的是，所得的分离角与Re=10^4-10^5范围内的实验测量结果相符。 显示英文摘要

摘要： We study the separating flow over a circular cylinder with two objectives: (i) to demonstrate the validity of the condition of matching curvature, and (ii) to obtain a reasonable estimate of the separation angle in the subcritical regime (Re=10^4-10^5) without explicitly modeling the boundary layer. First, we study Roshko's free streamline model (1954); it is an ideal flow model with sheets of discontinuities that represent the separating shear layers in the near wake region. The model fails to predict the correct separation angle over a cylinder. Roshko attributed this discrepancy to the condition of matching curvature, which asserts that the curvature of the separating streamline at the separation point must match that of the cylinder. We show that such a condition is legitimate and is not the real culprit for the failure of Roshko's model in predicting separation. Second, we employ the principle of minimum pressure gradient (PMPG), which asserts that, an incompressible flow evolves by minimizing the total magnitude of the pressure gradient over the domain. Encouraged by the fact that the flow characteristics in the range Re=10^4-10^5 are fairly independent of Re, we aim to predict the separation angle in this regime without modeling the boundary layer -- a task that may seem impossible, though anticipated by Prandtl in his seminal paper (Prandtl 1904). Over the family of kinematically-admissible, equilibrium flows, we utilize the PMPG to single out the separating flow with the minimum pressure gradient cost. Interestingly, the obtained separation angles match experimental measurements over the regime Re=10^4-10^5.