A two-dimensional passive structure undergoing symmetric hovering is conidered, and the associated flow field is examined by using proper orthogonal decomposition (POD) analysis. The dominant structures and patterns observed in the fluid are hierarchically ranked, and these structures are used to understand the peak aerodynamic efficiency realized for a particular choice of the wing stiffness. In ongoing work, a database of POD mode shapes is being used to characterize the flow across a range of parameters. The overall effort is aimed at exploiting the structures found in the POD modes and developing nonlinear phenomena based control to enhance aerodynamic performance.