Boundary layer flow over a bump and the three-dimensional law of the wall

Many turbulence theories in use today are based on two-dimensional equilibrium flows and have limitations when applied to three-dimensional flows. A three-dimensional law of the wall would help to improve simulation fidelity, but while several versions have been proposed, none have been widely accepted. In this study, the three-dimensional attached boundary layer flow over the windward side of the BeVERLI (Benchmark Validation Experiments for RANS/LES Investigations) Hill bump model was measured using near-wall laser Doppler velocimetry in the Virginia Tech Stability Wind Tunnel to study the mean flow and turbulence structure. These mean velocity measurements are compared with the predictions of the proposed three-dimensional (3D) law of the wall of van den Berg [A three-dimensional law of the wall for turbulent shear flows. J Fluid Mech. 1975;70(1):149-160.], which incorporates pressure gradients and inertial effects but assumes alignment of the mean flow gradient and shear-stress angles, and to the sublayer momentum equations, which are exact in the limit of wall-normal x(2)(+) -> 0. In regions with mild stress/strain misalignment, the van den Berg model compares favourably with the experimental data up to a maximum of x(2)(+) approximate to 800, and the sublayer momentum relationship compares favourably with the experimental data in the linear sublayer.