Partially-averaged Navier–Stokes simulations of turbulent flow past a square cylinder: Comparative assessment of statistics and coherent structures at different resolutions

Scale-resolving simulations of the turbulent wake behind a square cylinder are performed at Re = 22 000 using the partially averaged Navier–Stokes (PANS) k-ω closure model at different degrees of resolution (cut-off scales) corresponding to the unresolved-to-total kinetic energy ratio f_k ∈ [0.10, 0.50]. The two principle objectives of the study are to (i) establish the degree of resolution required for an accurate computation of different quantities of interest ranging from flow statistics to coherent structures and (ii) develop a protocol for a quantitative assessment and comparison of the large-scale coherent structures simulated at different degrees of resolution. Straightforward use of proper orthogonal decomposition (POD) to assess and compare large-scale coherence at different resolution levels can prove difficult as small-scale features can affect the POD mode shape and amplitude. To overcome this difficulty, two methods of quantifying coherent structures in the wake are proposed. These methods are based upon the incorporation of Fourier and Chebyshev decompositions with spectral proper orthogonal decomposition, respectively. We examine the first-mode energy spectra and the corresponding streamwise mode shapes using the results generated from PANS simulations at different degrees of resolution. It is demonstrated that increasingly finer resolutions are needed for integral quantities, one-point statistics, frequency spectra, and coherent structures, in that order. The underlying physics is explicated.