Wake-Induced Drag and Phase-Reconstructed Dynamics of a Flexible Plate in Normal Flow
Flexible structures in an incoming perpendicular flow typically undergo elastic reconfiguration that reduces drag; however, at higher velocities, they are prone to dynamical instabilities that entail complex wake dynamics and fluctuating loads. In this study, we investigate the wake of a thin, flexible plate clamped at its midpoint and oriented normal to an airflow, modelling reconfigurable natural systems such as trees and sea-grasses. By combining Proper Orthogonal Decomposition, Robust Principal Component Analysis, and Singular Value Decomposition with non-time-resolved Particle Image Velocimetry, we reconstruct the periodic coherent flow structures across both static and vibrating regimes. We demonstrate that structural oscillation symmetry directly dictates the wake topology. The symmetric vibration regime is characterised by two parallel 2S-type vortex shedding patterns on either side of the plate-herein termed the S-2S mode-whereas the antisymmetric regime exhibits a classic 2P-type shedding pattern. Furthermore, an impulse-based force analysis links these wake circulations to drag, revealing an additional mean drag penalty in the antisymmetric regime. Our approach offers a practical framework to extract and interpret coherent wake structures from limited temporal data, enhancing our understanding of fluid-structure interactions and informing aerodynamic load predictions.