Gravity currents flowing upslope: Laboratory experiments and shallow-water simulations

This paper investigates the dynamics of lock-release gravity currents propagating upslope by laboratory experiments and shallow-water simulations. Both the interface between the dense and the ambient fluid and the instantaneous velocity field were measured by image analysis. Different runs were carried out by varying the initial density of the lock fluid and the bed upslope. As a gravity current moves upslope, the dense layer becomes thinner, and an accumulation region of dense fluid in the initial part of the tank occurs. The current speed decreases as the bed upslope increases, and for the highest up sloping angles, the gravity current stops before reaching the end of the tank. A new two-layer shallow-water model is developed and benchmarked against laboratory experiments. The present model accounts for the mixing between the two layers, the free surface, and the space-time variations of the density. The effect of the horizontal density gradient in the simulation of gravity currents is investigated by comparing the numerical results of both the present model and the model proposed by Adduce et al. ["Gravity currents produced by lock-exchange: Experiments and simulations with a two layer shallow-water model with entrainment," J. Hydraul. Eng. 138, 111-121 (2012)] with laboratory measurements. The comparison shows that the present model reproduces both the current shape and the front position better than the Adduce et al. model, in particular, for gravity currents flowing up a slope. For these currents, the presence of a backflow near the lock is shown by the analysis of the streamwise depth-averaged velocity predicted by the present model and the velocity measured by particle image velocimetry as well.