Lock-release gravity currents and dam-break flows

Abstract

Gravity current and dam-break flows, resulting from the instantaneous release of fluid initially at rest behind a lock gate, are modelled theoretically using the shallow water equations. By analysing the motion in the hodograph plane, the governing equations become linear and hence it is possible to integrate them analytically from lock-release initial conditions. This approach provides many advantages: not only are numerical computations obviated, but the analysis clearly reveals how the nature of the ensuing flow depends on the Froude number, $\hbox{\it Fr}$, at the front of the current. It is also demonstrated that the motion comprises uniform and simple wave regions within which both or one of the characteristic variables are constant, respectively, in addition to complex wave regions within which both characteristic variables vary. These solutions reveal phenomena that have not previously been reported for gravity current flow. Specifically, when $\hbox{\it Fr}\,{>}\,2$, the height and velocity fields become discontinuous at late times at an interior point within the current. Conversely, when $\hbox{\it Fr}\,{<}\,2$, there is a wave-like disturbance that propagates along the length of the current, being reflected successively between the rear wall of the lock and the front of the flow.