Vol.:(0123456789) Environmental Fluid Mechanics https://doi.org/10.1007/s10652-019-09663-3 1 3 Velocity scales in steady‑nonuniform turbulent fows with low relative submergence D. Ferraro 1  · S. Servidio 2  · R. Gaudio 1 Received: 12 June 2018 / Accepted: 14 January 2019 © Springer Nature B.V. 2019 Abstract The most employed velocity scale in open-channel fows is the shear velocity. Although it is efortlessly identifed in uniform fow condition, its value becomes elusive to fnd in nonuniform fow condition. Furthermore, in low relative submergence fows, the absence of the universal log-law velocity distribution eliminates the methods which exploit the log- arithmic velocity profles in order to compute the shear velocity. The aim of this work is to fnd a tool to compute a better scaling velocity in uniform and nonuniform fows with low relative submergence. In particular, laboratory tests were performed and the characteris- tics velocities were computed through the momentum balance, the kinetic energy balance and the 4/5 law of turbulence. These velocity scales were compared for the frst time in fows with low relative submergence, showing that the best velocity scale can be obtained through the application of the well-known Kolmogorov 4/5 law. This study is focused on possible applications to the natural environment, where indeed the bed type is highly inho- mogeneous and irregular. The results obtained with the acoustic Doppler velocimeter tech- nique suggest that accurate measurements and analysis are fundamental not only in labora- tory settings but also in natural environment fows. Keywords Turbulence · Open channel fow · Kolmogorov law 1 Introduction The shear velocity is one of the most important characteristic velocities in open-channel fows. This velocity scale is usually computed in uniform fow condition, but its assessment is still debated in nonuniform fows. Its defnition is even more difcult in fows with low relative submergence (ratio between water depth and roughness height). Nonuniform fow conditions and low relative submergence are often simultaneously observed in mountain streams, in which the roughness elements have a comparable length with respect to the water depth. In order to identify the above velocity scale, several methods has been pro- posed in the literature under the well-known hypothesis of universal logarithmic velocity * D. Ferraro domenico.ferraro@unical.it 1 Dipartimento di Ingegneria Civile, Università della Calabria, 87036 Rende, CS, Italy 2 Dipartimento di Fisica, Università della Calabria, 87036 Rende, CS, Italy