  A networked oscillator based analysis is performed for periodic bluff body
flows to examine and control the transfer of kinetic energy. Spatial modes
extracted from the flow field with corresponding amplitudes form a set of
oscillators describing unsteady fluctuations. These oscillators are connected
through a network that captures the energy exchanges amongst them. To extract
the network of interactions among oscillators, amplitude and phase
perturbations are impulsively introduced to the oscillators and the ensuing
dynamics are analyzed. Using linear regression techniques, a networked
oscillator model is constructed that reveals energy transfers and phase
interactions among the modes. The model captures the nonlinear interactions
amongst the modal oscillators through a linear approximation. A large
collection of system responses are aggregated into a network model that
captures interactions for general perturbations. The networked oscillator model
describes the modal perturbation dynamics better than the empirical Galerkin
reduced-order models. A model-based feedback controller is then designed to
suppress modal amplitudes and the resulting wake unsteadiness leading to drag
reduction. The strength of the proposed approach is demonstrated for a
canonical example of two- dimensional unsteady flow over a circular cylinder.
The present formulation enables the characterization of modal interactions to
control fundamental energy transfers in unsteady vortical flows.
