The flow over two-dimensional geometries is studied via unsteady numerical simulations that are three dimensional, with periodic conditions applied along the spanwise coordinate. This framework is well accepted for direct numerical simulations (DNS), large-eddy simulations, and detached-eddy simulations (DES), but is here combined with standard Reynolds-averaged Navier–Stokes (RANS) turbulence models. This strategy, which is not new, is referred to as unsteady RANS (URANS). Limited previous evidence suggested that, in URANS, three dimensionality is suppressed by high eddy-viscosity levels. However, three dimensionality proves fairly easy to sustain with adequate initial conditions, in all three cases studied here: stalled airfoil, circular cylinder, and a rounded square, except that for one case three dimensionality failed to last from random-based initial perturbations and was sustained only when using a DES field as initial condition. It is much less fine grained and chaotic than in the classical turbulence-resolving methods (from DNS to DES). Three-dimensional URANS gives clear improvements over two-dimensional URANS. It is less costly than DES, but is not as accurate. URANS also displays a troublesome sensitivity to the spanwise period and to the turbulence model. The approach is interesting and will appear spontaneously in many applications, but remains only partly understood.