Force decomposition on flapping flexible plate via impulse theory and dynamic mode decomposition

Dynamic mode decomposition (DMD) is a widely used method to extract dynamic information from sequential flow data, aiding our comprehension of fluid dynamics and transport processes. While DMD can unveil internal system laws and predict unsteady flow phenomena, the connection between DMD modes and the nonlinear hydrodynamic behavior of solid bodies remains unexplored. This study investigated the internal relationship between DMD modes and their impact on hydrodynamic forces. We employed a penalty-immersed boundary method to simulate the behavior of a flapping flexible plate in a uniform incoming flow, generating extensive datasets of vorticity fields. By applying DMD to these datasets, we identified key modes governing the flow dynamics, including the shear layer, symmetric vortex street, and antisymmetric vortex street. Furthermore, we utilized the impulse theory to analyze the force characteristics of the plate based on the corresponding DMD modes. The net force is determined by the combined contributions of the impulse force and the vortex force. Our findings reveal that the net horizontal force is primarily influenced by the first two modes. Specifically, mode 1, characterized by a dimensionless frequency of f * = 0, contributes to thrust, whereas mode 2, with f * = 1, contributes to drag. This physical investigation holds relevance for fluid-structure systems involving the interaction dynamics of flexible structures with unsteady wake vortex systems.