We present experimental results on the development of gravity currents moving onto sloping boundaries with slope angles $\unicode[STIX]{x1D703}=7^{\circ }$, $10^{\circ }$ and $15^{\circ }$. Different regimes of flow development are observed depending on the slope angle and on the initial velocity and density profiles, characterized by the Richardson number $J_{i}=\unicode[STIX]{x1D6FF}_{i}{g_{0}}^{\prime }/\unicode[STIX]{x0394}u_{i}^{2}$, where $\unicode[STIX]{x1D6FF}_{i}$, $\unicode[STIX]{x0394}u_{i}$ and $g_{0}^{\prime }$ are, respectively, the velocity interface thickness, the maximum velocity difference and reduced gravity at the beginning of the slope. For $J_{i}>0.7$ and the larger slope angle, the flow strongly accelerates, reaches a maximum at the beginning of the Kelvin–Helmholtz instability, then decelerates and re-accelerates again. For $0.3<J_{i}<0.6$, instability occurs earlier and velocity oscillations are less. When $J_{i}\leqslant 0.3$ the increase in velocity is smooth. The magnitude of velocity oscillation depends on the combined effect of $J_{i}$ and slope angle, expressed by an overall acceleration parameter $\overline{T_{a}}=(\unicode[STIX]{x1D6FF}_{i}/U_{i})((U_{c}-U_{i})/x_{c})$, which, to first order, is given by $J_{i}\sin \unicode[STIX]{x1D703}$, where $U_{c}$ and $x_{c}$ are, respectively, the velocity and position at instability onset. The velocity increases smoothly up to an equilibrium state when $\overline{T_{a}}\leqslant 0.06$ and exhibits an irregular behaviour at larger values of $\overline{T_{a}}$. The critical Richardson number $J_{c}$ decreases with increasing $J_{i}$ (increasing $\unicode[STIX]{x1D6FF}_{i}/h_{i}$) which is due to wall effects and $\unicode[STIX]{x1D6FF}/\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D70C}}\neq 1$. After the beginning of Kelvin–Helmholtz instability, entrainment rates are close to those of a mixing layer, decreasing to values of a gravity current after the mixing layer reaches the boundary. It is shown here that the interfacial instability during current development affects the bottom shear stress which can reach values of $c_{D}\approx 0.03$ regardless of initial conditions. By solving numerically the depth integrated governing equations, the gravity flow velocity, depth and buoyant acceleration in the flow direction can be well predicted for all the performed experiments over the full measurement domain. The numerical results for the experiments with $J_{i}>0.3$ predict that the current requires a distance of at least $x_{n}\approx 40h_{i}$ to reach a normal state of constant velocity, which is much larger than the distance $x_{n}\approx 10h_{i}$ required in the case of a current with $J_{i}\leqslant 0.3$ that is commonly assumed for downslope currents.

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 ξ N of the nose. The predicted u N increases with time and distance ξ from the ridge. Since Ri decreases with ξ 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.

We consider a gravity current released from a lock into an ambient flui of smaller density, that, from the beginning or after some horizontal propagation X 1 , propagates along an inclined (up-or down-) bottom. The flo (assumed in the inertial-buoyancy regime) is modeled by the shallow-water (SW) equations with a jump condition applied at the nose (front). The behavior of the current is dominated by the slope angle, θ, but is also affected by additional dimensionless parameters: the aspect ratio of the lock x 0 /h 0 , the height ratio of the ambient to lock, H/h 0 , and the distance of the backwall from the beginning of the slope, X 1 /x 0. We show that the stability of the interface, reflecte by the value of the bulk Richardson number, Ri, is essential in the interpretation and modeling. In the upslope flow Ri increases and hence entrainment/mixing effects are unimportant. In the downslope flow the current firs accelerates and Ri decreases; this enhances entrainment and drag, which then decelerate the current. We show that the accelerating-decelerating downstream current is reproduced well by a SW model combined with a simple closure for the entrainment and drag. A comparison of the theoretical results with previously published experimental data for both upslope flo and downslope flo show fair agreement.