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We present a new method for generating robust guesses for unstable periodicorbits (UPOs) by post-processing turbulent data using dynamic modedecomposition (DMD). The approach relies on the identification of near-neutral,repeated harmonics in the DMD eigenvalue spectrum from which both an estimatefor the period of a nearby UPO and a guess for the velocity field can beconstructed. In this way, the signature of a UPO can be identified in a shorttime series without the need for a near recurrence to occur, which is aconsiderable drawback to recurrent flow analysis, the current state-of-the-art.We first demonstrate the method by applying it to a known (simple) UPO and findthat the period can be reliably extracted even for time windows of length onequarter of the full period. We then turn to a long turbulent trajectory,sliding an observation window through the time series and performing many DMDcomputations. Our approach yields many more converged periodic orbits(including multiple new solutions) than a standard recurrent flow analysis ofthe same data. Furthermore, it also yields converged UPOs at points where therecurrent flow analysis flagged a near recurrence but the Newton solver did notconverge, suggesting that the new approach can be used alongside the old togenerate improved initial guesses. Finally, we discuss some heuristics on whatconstitutes a "good" time window for the DMD to identify a UPO.

Searching turbulence for periodic orbits with dynamic mode decomposition