Gravity currents propagating up a slope in a two-layer fluid

Abstract

Gravity currents produced by partial-depth lock-release and travelling along the base of a two-layer stratified ambient are investigated as they propagate along a rising slope. The initial gravity current front speed is found to be consistent with a theory adapted from Shin et al. [“Gravity currents produced by lock exchange,” J. Fluid Mech. 521, 1-34 (2004)] to the case of partial-depth currents in two-layer ambients. The subsequent evolution depends on the gravity current speed relative to the speed of the interfacial disturbance it creates. The deceleration of supercritical gravity currents, which travel faster than the interfacial disturbance, is gradual and agrees well with the relationship developed by Marleau et al. [“Gravity currents propagating up a slope,” Phys. Fluids 26, 046605 (2014)] for upslope gravity currents in uniform density ambients. In several subcritical cases, the gravity current suddenly came to rest as a consequence of interactions with the interfacial disturbance. The disturbance amplitude, speed, and width are found to be nearly constant during its evolution. In cases for which the ambient interface intersected the bottom slope, the amplitude, speed, and width were nearly constant up to the point where the lower layer shallowed and the disturbance transformed into an upslope-propagating gravity current.