The unsteady overtopping of barriers by gravity currents and dam-break flows

Edward W. G. Skevington, Andrew J. Hogg

Published 2022-10-14Version 1

The collision of a gravitationally-driven horizontal current with a barrier following release from a confining lock is investigated using a shallow water model of the motion, together with a sophisticated boundary condition capturing local properties of the interaction. The boundary condition permits several overtopping modes: supercritical, subcritical, and blocked flow. The model is analysed both mathematically and numerically to reveal aspects of the unsteady motion and to compute the proportion of the fluid trapped upstream of the barrier. Several problems are treated. Firstly, the idealised problem of a uniform incident current is analysed to classify the unsteady dynamical regimes. Then, the extreme regimes of a very close or distant barrier are tackled, showing the progression of the interaction through the overtopping modes. Finally, the trapped volume of fluid at late times is investigated numerically, demonstrating regimes where the volume is determined purely by volumetric considerations, and others where transient inertial effects are significant. For a Boussinesq gravity current, approximately $30\%$ of the fluid escapes the domain even when the volume of the region confined by the barrier is equal to the fluid volume, and a confined volume $3$ times larger is required to stop the majority of the fluid. For a non-Boussinesq current, the value is in excess of $60\%$, and a barrier as tall as the initial release is required to retain most of the fluid. Finally, we compare our predictions to experiments, showing a good agreement across a range of parameters for dam-break flows.