Elucidating the 3D topology of a cantilevered square cylinder wake using multi-time-delay estimation with FIR-based SPOD*

FIR-based spectral proper orthogonal decomposition (SPOD) (Sieber et al., 2016) is used for remote-sensor based estimation of a highly modulated bluff body wakes. The estimator is trained on individual stereoscopic particle image velocimetry (PIV) planes synchronized with surface pressure measurements. Estimation is then used to reconstruct time-resolved 3D coherent motions with the aim of investigating cycle-to-cycle variations in vortex interactions. The candidate flow is the near turbulent, quasi-periodic near-wake of a cantilevered square cylinder with a height-to-width ratio 4, protruding a thin laminar boundary layer at a Reynolds number of 10600. In a phase-averaged sense, the wake is described as a half-loop shedding pattern, consisting of inter-connected Kármán vortex structures.

We show the benefits of this convolutional SPOD in reconstructing the flow and identifying coherent wake interactions. Unlike phase-averaging, which provides only a representation of the average contributions at the fundamental Kármán shedding frequency (f_s) and its harmonics, the present approach also captures slow-varying motions at f_L = 0.1f_s and inter-harmonic contributions. The slow-varying motion, which arises from shear layer instabilities originating at the obstacle free-end, is shown to modulate intensity of the fundamental vortex-shedding. Inclusion of the inter-harmonic modes allows capturing of shedding disruptions, which in extreme cases manifest as vortex dislocations.