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.

Analyzed in the paper are three-dimensional complex-chemistry direct numerical simulation data obtained from lean hydrogen–air flames under various conditions (25 cases; equivalence ratios ϕ=0.35 and 0.5; the normalized root mean square velocity 0.25≤u′/SL≤54.1; the normalized turbulence length scale 0.5≤L/δLT≤2.6; and Karlovitz number 1.0≤Ka≤1315, where SL and δLT are laminar flame speed and thickness, respectively). These data are supplemented with data obtained in two-dimensional and three-dimensional complex-chemistry simulations of unstable laminar flames in the same computational domains. The reported results show that diffusional-thermal instability (DTIns) dominates turbulence in three weakly turbulent flames (Ka≤1.5). In more intense turbulence, burning rate is still significantly increased by differential diffusion effects, but manifestations of DTIns appear to be less pronounced. Specifically, (i) contribution of highly curved reaction zones (curvature radius is smaller than the instability neutral wavelength) to the bulk burning rate is significantly increased with increasing u′/SL and Ka, (ii) amplitudes of local perturbations in the equivalence ratio, temperature, fuel consumption, or heat release rate are significantly different in unstable laminar and turbulent flames, and (iii) bulk burning rates are also significantly different. The emphasized differences are increased with increasing u′/SL and Ka. These trends imply a decreasing role played by DTIns in turbulent flames at higher Karlovitz numbers, whereas differential diffusion effects result in significantly increasing bulk burning rate at Ka as large as 1315.