Propagation of a continuously supplied gravity current head down bottom slopes

We present a combined theoretical-experimental investigation of the downslope propagation of a gravity current sustained by a source. The current propagates first on a horizontal bottom, then on a downslope. We focus on the case when the current at the ridge (point where donwslope begins) has a stable interface (Ri > 0.25) and is critical with F = 1, where Ri and F are the bulk Richardson and flow Froude numbers. We derive the equations that govern the nose propagation and speed using a shallow-water (SW) model, in which the nose is a jump matched to characteristics emitted at the ridge. This provides a self-contained prediction for the speed of propagation u(N) and position xi(N) of the nose. The predicted u(N) increases with time and distance xi from the ridge. Since Ri decreases with xi in the tail behind the nose, appearance of instabilities at a certain traveled distance determines the domain of validity of the SW solution. A good agreement is reported with various experiments with different initial conditions at the ridge and slope angles (both fixed and changing with distance from the ridge). It is shown that the nose velocity is always less than the maximum velocity within the current head, which corresponds to the speed of the characteristics released at the ridge that catch on the current head.