Scour evolution downstream of grade-control structures under unsteady flows: A theoretical analysis

River restoration projects often make use of grade-control structures in order to prevent channel degradation, improve their ecological resources, and regulate floods. The time evolution of localized scour that can occur downstream of grade-control structures represents a crucial component in the design of those projects. This is because erosion processes may undermine the stability of hydraulic structures and compromise their effectiveness. Although localized scour has been widely investigated (mostly via laboratory models), there is significant scatter in results produced by the large number of obtained empirical equations. Consequently, there is a need for more general tools based on theoretical approaches that might overcome the limits of ad-hoc, experimental methods. In particular, a model based on the application of the Phenomenological Theory of Turbulence (PTT) has been recently developed by the last three authors to predict scour-depth evolution under steady flows. Nevertheless, in practical applications, scour phenomena usually occur during floods characterized by variable flow discharges. In this paper, for the first time to the authors’ knowledge, a detailed analysis of the basic assumptions of the PTT-evolution model allowed us to assess their validity for scour processes at different grade-control structures under unsteady (time-dependent) flows. By re-analyzing the dynamics of the scour evolution under unsteady flow conditions, we corroborate its consistency with the steady counterpart and with jet-driven scour problems, evincing that a homothetical evolution of the scour hole occurs during the developed phase. Finally, we provide a confirmation of the general validity of the theoretical approach presented herein. We show that it can be successfully applied to a large range of structure configurations and hydraulic conditions, without any significant modification. This last result is particularly important, since it paves the way to a unique, first-principles-based tool that can be helpful to design hydraulic structures.