Generalised phase average with applications to sensor-based flow estimation of the wall-mounted square cylinder wake

We experimentally investigate the three-dimensional wake behind a finite wall-mounted square cylinder at $Re=12,000$ and aspect ratio of $4$. Focus is placed on the base flow and oscillatory fluctuation. Time-resolved 3D velocity fields are constructed from high-frame-rate particle image velocimetry (PIV) and simulatenously recorded surface pressure measurements. All three velocity components are resolved in a rectangular near-wake region by two orthogonal dense arrays of parallel PIV planes. A key enabler is a generalized phase-average incorporating slowly varying base flow, a variable oscillation amplitude and higher harmonics. These generalizations reduce the residual 30\% below those of a traditional phase average. Moreover, the resolved variations reveal analytical constraints of the mean flow and oscillation levels, like the mean-field paraboloid. The proposed methodology for generalized phase averaging and for construction of 3D velocity fields from 2D PIV data is applicable to a large class of turbulent flows with oscillatory dynamics.