The Kinematics of Lagrangian Flow Separation in External Aerodynamics

Abstract: 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.