本文在拉格朗日坐标系下研究了外部空气动力学中流动分离的运动学问题。具体而言，从壁面上涌的流体材料的初始运动与流场中的长期吸引歧管有关。虽然短时间的运动学是由形成的材料尖峰上游的零表面摩擦点和喷射的粒子在渐近分离线的方向，流体示踪剂的轨迹被引导吸引脊的有限时间李雅普诺夫指数，一旦他们离开附近的壁。这种初始流体上涌事件的壁特征，即所谓的\textit{spiking point} [Serra，M.，Vetel，J.，Haller，G.，“Exact theory of material spike formation in flow separation”，\textit{J. Fluid Mech.}，Vol. 845，2018]，根据平流物质线的曲率计算，并首次根据从圆柱体和弯曲NACA 65（1）-412翼型的直接数值模拟获得的壁法向速度的高阶数值导数计算。由于翼型轮廓的基于样条的边界参数化引起振荡，因此可以通过适当的滤波鲁棒地恢复主尖峰点。短期运动学与边界层中的标度长度密切相关。
英文摘要：
Kinematic aspects of flow separation in external aerodynamics are investigated in the Lagrangian frame. Specifically, the initial motion of upwelling fluid material from the wall is related to the long-term attracting manifolds in the flow field. While the short-time kinematics are governed by the formation of a material spike upstream of the zero-skin-friction point and ejection of particles in direction of the asymptotic separation line, the trajectories of the fluid tracers are guided by attracting ridges in the finite-time Lyapunov exponents once they leave the vicinity of the wall. The wall signature of this initial fluid upwelling event, the so-called \textit{spiking point} [Serra, M., Vetel, J., Haller, G., "Exact theory of material spike formation in flow separation", \textit{J. Fluid Mech.}, Vol. 845, 2018], is computed from the curvature of advected material lines and, for the first time, from high-order numerical derivatives of the wall-normal velocity obtained from direct numerical simulations of a circular cylinder and a cambered NACA 65(1)-412 airfoil. As the spline-based boundary parametrization of the airfoil profile induces oscillations, the principle spiking point can be recovered robustly through appropriate filtering. The short-term kinematics correlate strongly with the scaling lengths in the boundary layer.
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Lagrangian dynamics unveil polymer conformation in viscoelastic flows
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Residual sweeping effect in turbulent particle pair diffusion in a Lagrangian diffusion model
Thomson，D. J. \& Devenish，B. J. [{ \em J.~流体机械526，277（2005）]和其他人已经提出，在运动学模拟（KS）中，扫掠效应使得拉格朗日性质，Fung等人[Fung J. C. H、亨特·J·C。R.，马利克·N A.帕金斯R. J. { \em}流体机械236，281（1992）]，不可靠。在这里，它是通过一个新的分析的基础上分析的参考帧中的粒子轨迹移动的大能量包含的运动尺度，在湍流对扩散率（$K$）由于清扫效果的归一化综合误差$e^I_K$随着增加对分离（$σ_l$），使$e^I_K\to 0$为$σ_l/η\to \infty$ ;和$e^I_K\to \infty$为$σ_l/η\to 0$。$η$是Kolmogorov湍流微尺度。存在一个中间分离范围$1<σ_l/η< \infty$，其中误差$e^I_K$保持可忽略。使用KS的模拟表明，在扫频参考系中，该中间范围很大，几乎覆盖了整个模拟的惯性子范围$1<σ_l/η< 10^5$，这意味着在KS中观察到的局部偏差因此不能归因于扫频误差，并且可能是真实的。这对于对扩散理论和建模非常重要。
