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Motivated by closed-loop flow control applications, a new formulation of the proper orthogonal decomposition (POD) is presented which is capable of characterizing not only the controlled and natural states of a given flow but also the transient behavior between these states. This approach, which is termed temporal POD (TPOD) extracts the optimum frameof-reference and the temporal information regarding the dynamics of the system in the presence of the flow control. The TPOD concept is developed in this paper and demonstrated experimentally in an application involving a circular cylinder in cross flow at ReD = 5,000 with active plasma flow control. The resulting model is shown to properly capture the correct dynamics of the first TPOD mode, including the natural, forced and transient regimes.

A Temporal Proper Orthogonal Decomposition (TPOD) Method for Closed-Loop Flow Control