The Phenomenological Theory of Turbulence and the Scour Evolution Downstream of Grade-Control Structures under Steady Discharges

A more complete understanding of scour mechanisms for flows downstream of grade-control structures, including their temporal evolution, has the potential to lead to improved predicting tools for design. To date, design equations have been mostly derived empirically, i.e., by parametric modelling (at generally-small scales) corresponding to specific structure configurations, and for limited ranges of hydraulic conditions. Although these approaches allowed different authors to propose many empirical and/or semi-empirical equations, they lack generality and may lead to incorrect estimations when applied outside their ranges of validity. First-principles-based methods with solid calibration and validation procedures can overcome these issues. Following recent theoretical advancements presented elsewhere by the last three authors, in this work we analyze and test the predictive capability of a scour evolution model based on the phenomenological theory of turbulence (PTT) by using a large dataset pertaining to different grade-control structures. Although the PTT model was developed (and validated) for scour evolution caused by oblique and vertical plunging jets, we show that its basic assumptions are still valid for the addressed low-head structures, encompassing rock structures, stepped gabion weirs, rock and bed sills, and others. Furthermore, we also provide interesting insights on scour evolution by contrasting the predicting capability of our model against experimental data by different authors for specific structures. Results of the comparison conclusively show that the PTT model has a general validity and represents a trustable tool to estimate scour evolution regardless of the structure configuration and hydraulic conditions.