Application of SPOD analysis to PIV data obtained in the wake of a circular cylinder undergoing vortex induced vibrations

Vortex induced vibrations (VIV) of a circular cylinder have been investigated experimentally using a cyberphysical apparatus with m∗ = 8, ζ = 0.005, and Re = 4000. This study considers the application of proper orthogonal decomposition (POD) and spectral POD (SPOD) analysis to the wake dynamics of the low-mass-ratio VIV of a circular cylinder in the lower branch at U∗ = 7.5. SPOD has been previously shown to better separate frequency-centered modal dynamics, compared to POD. Coherent POD and SPOD modes were compared and the newly separated third SPOD mode pair was found to have a periodicity characteristic of vortex shedding and a peak in the temporal coefficient spectra at St = f D/U∞ = 0.2248. The literature has identified that the wake dynamics within the lower branch are synchronized to the cylinder motion; however the present study suggests that some hidden dynamics persist at the Strouhal frequency. Low order models based on the first eight POD and SPOD modes were compared, and it was found that the filtering operation in SPOD removes the uncorrelated stochastic energy component of the POD modes while producing a comparable representation of the coherent deterministic part of the wake dynamics. Using SPOD to separate the distinct frequency-centered dynamics into unique, interpretable mode pairs will simplify future efforts to develop sparse dynamical models of the flow.