Shallow water hydrodynamics: Surge propagation and sill-controlled flows

Abstract

Accurate flow models are crucial for simulating shallow water hydrodynamics, particularly in predicting and mitigating the impacts of extreme events involving free-surface flows. Many of these extreme scenarios in river environments involve fluid dynamics with significant dynamic pressures, invalidating the use of standard Saint-Venant-type models. This study presents a robust and accurate novel alternative based on the Reynolds-averaged Navier-Stokes (RANS) equations solved through variational methods. Despite their potential, variational methods have been underutilized in the literature, and their application has been limited to low-level expansions. Moreover, they are rarely validated against experiments that simulate complex flows. This study addresses both challenges. First, a general mathematical framework is developed for the variational RANS (VR) model of arbitrary high-level. The VR level III model is presented and is solved numerically using a robust finite volume-finite difference solver for turbulence flow modeling. Second, an extensive experimental program was conducted to validate this new flow modeling tool, focusing on two challenging flow scenarios. The first scenario involves the propagation of turbulent breaking waves over an irregular, uneven bathymetry—conditions similar to those observed during bedform development in riverine environments. This scenario involved the experimental characterization of unsteady surges over an array of obstacles in series. The second scenario investigated sill-controlled released discharges, similar to those occurring in estuary inlets with sediment bars. Comparisons between the new experimental data and the predictions from the VR level III model reveal the model’s accuracy and robustness, making it a highly suitable tool for simulating free-surface flows.