  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
the local 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. Next, the trapped
volume of fluid at late times is investigated numerically, demonstrating
regimes in which the volume is determined purely by volumetric considerations,
and others where transient inertial effects are significant. For a Boussinesq
gravity current, even when the volume of the confined region behind the barrier
is equal to the fluid volume, $30\%$ of the fluid escapes the domain, and a
confined volume $3$ times larger is required for the overtopped volume to be
negligible. For a subaerial dam-break flow, the proportion that escapes is in
excess of $60\%$ when the confined volume equals the fluid volume, and a
barrier as tall as the initial release is required for negligible overtopping.
Finally, we compare our predictions to experiments, showing a good agreement
across a range of parameters.
