Scaling turbulent wake flow downstream of isolated piers in laboratory and river

• Experiments were conducted in the laboratory and field on pier model and prototype. • The ratio between water level drop and pier width, S vh , was introduced as scale. Turbulent variables like power spectral and integral length scales were determined. • At constant Froude, S vh scales the turbulent spectra with turbulent viscosity • Applying this procedure to Leonardo da Vinci’s drawings allowed to estimate its visual acuity The flow around a bridge pier is a classic example of fluid-structure interaction in hydraulics where different phenomena coexist, namely: contraction of the flow section, vortex ejection, generation of horse-shoe vortexes and possible bed erosion. Knowing how the fluid and pier interact, and the role of the generated turbulent wake is crucial for the design of stable bridges and riverbeds. Physical modelling in the laboratory together with numerical modelling are two important tools to address the study of the flow around the bridge pier. Results from physical modelling in reduced scale models must be transferred to prototype obeying similarity criteria defined by the appropriate non-dimensional parameters such as Reynolds and Froude numbers. This paper presents an investigation on scaling turbulent wake flows downstream of isolated piers based on the ratio between the water level drop and the obstacle’s flow facing width. Turbulent flow measurements were carried out both on scale models of different geometries of bridge piers in the hydraulics laboratory and around a real bridge pier at the Po River in Italy. The proposed scaling is applied to Leonardo da Vinci’s drawings of turbulent flow past a vertical obstacle aiming at providing insights and quantitative information about his drawings.