Phase-averaging of temporally uncorrelated PIV snapshots using Input/Output analysis

Abstract We present a method to estimate a flow's spectral content from temporally uncorrelated PIV snapshots by projecting them onto bases of modes obtained from Input/Output (I/O) analysis. Our method applies the linearized Navier--Stokes equations to mean fields and second-order turbulence statistics obtained from ensemble-averages of the experimental data to yield a set of modes across frequencies. Applying a regularized form of L"owdin orthogonalization, we obtain a basis onto which original snapshots can be projected to estimate likely frequencies and corresponding phase-averaged coherent modes in the flow. We apply our method to PIV measurements and corresponding simulations of flow past a spanwise cylinder embedded in a turbulent boundary layer with $Re_\tau = 1320$. While the cylinder sheds regular vortices into its wake, these coherent motions are strongly influenced by the chaotic nature of the background turbulence in the boundary layer. To vary the relative strength of this influence, the experiment and simulations were repeated with cylinders of $D/\delta = 0.045$ and $0.09$ at a gap width of $G/\delta = 0.09$. In both cases, our method recovers frequencies and coherent flow features, even though the influence of the background turbulence may be quite strong.