Estimating turbulent statistics from pairwise data

Modal analysis in space and time is important to understand the underlying physics of turbulence. However, many modal analysis techniques are limited to sequential data sets with a constant acquisition frequency. This is particularly challenging when using particle image velocimetry (PIV) flow data, where the capture rate may be slower than the required Nyquist frequency of the turbulence. However, if two PIV systems operate in tandem, pairs of data can be acquired that are arbitrarily close in time. The present work explores estimating spectral quantities from pairwise data, up to the Nyquist frequency of the small-time step within a pair. Several techniques will be investigated, including leveraging the relationship between Dynamic Mode Decomposition (DMD) and Spectral Proper Orthogonal Decomposition (SPOD) to estimate turbulent statistics. Current results show we can use DMD to estimate SPOD modes of a turbulent jet up to the Nyquist rate with up to 80 percent less data.