The strength of traditional spectral methods in turbulent direct numerical simulations (DNSs) of simple geometries have led to a focus on canonical configurations such as the plane channel and the zero pressure gradient (ZPG) boundary layer. The spectral element method (SEM), developed in the 1980s and progressively more widely used in the recent years through the numerical code Nek5000 (Fischer et al.), adds geometrical complexity to the spectral accuracy. This allows the simulation of more complicated flows.

Here we present both experimental and computational results of several non-canonical geometries, and exploit the capabilities of the SEM. We start by highlighting the importance of width-to-height ratio (AR) and flow development length in experiments of turbulent duct flows by analyzing oil film interferometry (OFI) and streamwise pressure gradient measurements. These experiments are complemented with DNSs of rectangular duct flows which serve as a platform to assess the effect of the secondary flow of second kind on wall-bounded turbulence. Direct numerical simulations of two external flows are presented next: a wall-mounted square cylinder of aspect ratio 4 and a wing section represented by a NACA4412 profile at Re=400,000. In the first case the emphasis is on the effect of inflow conditions (fully-turbulent or laminar) on the separated wake, whereas in the second one the effects of pressure gradient and surface curvature on wall-bounded turbulence are analyzed.