Recurrence analysis and time extrapolation of a confined turbulent jet using modal decomposition

We investigated the long-term dynamics of a turbulent, submerged jet at Re = 16 400 to develop a strategy for data-assisted, fast calculations of passive species transport. We obtained our data from high-fidelity large eddy simulations LES, which we validated against in-house particle image velocimetry measurements. The flow was split into coherent and incoherent fields using the method of proper orthogonal decomposition (POD). Depending on the number of POD modes to construct coherent velocity fields, different patterns in the recurrence plot of the system were found. For low mode numbers, line segments parallel to the main diagonal were present, which indicated that close states evolved similarly for a finite duration. Strong turbulent fluctuations in the original velocity fields, on the other hand, hid any large-scale recurrences and caused a structureless recurrence statistics. Using an iterated method of analogs, we time-extrapolated a short time series of coherent, distinctly recurring velocity fields of50 sto250 sand performed a study of species transport. We found that coherent dynamics alone could not reproduce LES results due to the lack of turbulent, small-scale fluctuations, but already a small set of incoherent flow fields sufficed to cure this shortcoming considerably. Surprisingly, time extrapolation of the original database without decomposition and without any obvious recurrences led to the best results in very close agreement with LES but with high demands regarding memory. Our data-assisted simulations outperformed LES on the same computational mesh by a speed-up factor of 15.