Bed scouring downstream of hydraulic structures under steady flow conditions: Experimental analysis of space and time scales and implications for mathematical modeling

Sediment transport and bed deformation in alluvial rivers are space and time dependent. The knowledge of the space and time scales can be helpful for the definition of predictive procedures of an alluvial reach response to changing boundary conditions. In this work, attention is paid to scouring process occurring downstream of the rigid basement of a hydraulic structure. The analysis is focused on transient bed profiles which are determined, under steady flow conditions, by a decrease of the upstream sediment transport rate. In particular, the paper is aimed at improving understanding of the space and time scales required by the alluvial system to reach the equilibrium conditions. For this purpose, movable-bed runs are carried out in a straight laboratory channel, for two values of the water discharge. During each run, the longitudinal bed profiles are measured at different times. Based on experimental data, spatial scale factors of the bed scouring and of the bed load transport to reach the equilibrium conditions are defined. Particularly, it is found that the scour length varies especially during the first evolution phase and then it oscillates around of a mean value that is about 40% of the channel reach interested by the phenomenon under consideration; an expression is found for the adaptation coefficient which allows the estimation of the spatial delay of the bed load transport rate. Using both the collected data and literature data an expression defining the time scale of scouring is deducted. According to this expression the non-dimensional time scale is related to Shields parameter through an exponential law. Then, by the help of a 1-D numerical model previously developed by the writer, the implications for choosing the spatial and temporal resolutions, on which numerical results depend significantly, are shortly discussed. The results show that the time and space scales, which represent physical constraints of the spatial and temporal resolutions, need to be properly defined in order to simulate the scouring process evolution.

Research Highlights
► On the basis of experimental data spatial scaling variable of scouring is defined
► An exponential expression is found for the time scale in non-dimensional form
► An expression is found for the adaptation coefficient in bed load transport estimation.
► The importance of spatial and temporal scale in scouring simulation is verified.